Discrete curve theory in space forms: planar elastic and area-constrained elastic curves | Paper Citation Record

Observation 86f69463-8cb4-4db9-b979-cd311a258d1b · outbound

This paper cites Constant mean curvature tori in terms of elliptic functions.Journal für die reine und angewandte Mathematik, 374:169–192, 1987.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Constant mean curvature tori in terms of elliptic functions.Journal für die reine und angewandte Mathematik, 374:169–192, 1987

Reference 1

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This paper cites Integrable dynamics in projective geometry via dimers and triple crossing diagram maps on the cylinder.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Integrable dynamics in projective geometry via dimers and triple crossing diagram maps on the cylinder

Reference 2

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Observation 39c9ffa1-125c-4a9f-91ce-6e78d4a91ff1 · outbound

This paper cites Cross-ratio dynamics on ideal polygons.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Cross-ratio dynamics on ideal polygons

Reference 3

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Observation 8c830f2e-d492-42cb-a103-16372b5ef9b9 · outbound

This paper cites Area-constrained planar elastica.Phys.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Area-constrained planar elastica.Phys

Reference 4

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Observation 2c89c87c-8b76-4818-a21f-372390fcfa59 · outbound

This paper cites Discrete elastic rods.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete elastic rods

Reference 5

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Observation 7227adaf-26a6-4ef8-bfb4-a5596f0a5986 · outbound

This paper cites Vorlesungen über Differentialgeometrie III.Springer Grundlehren XXIX, 1929.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Vorlesungen über Differentialgeometrie III.Springer Grundlehren XXIX, 1929

Reference 6

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Observation 00a4e8ba-7761-494c-b126-a43ab3d3516d · outbound

This paper cites Isothermic tori with one family of planar curvature lines and area constrained hyperbolic elastica.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Isothermic tori with one family of planar curvature lines and area constrained hyperbolic elastica

Reference 7

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Observation 0dfff5c3-cde4-471f-bbed-9ac533fe81bf · outbound

This paper cites Bobenko and Ulrich Pinkall.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Bobenko and Ulrich Pinkall

Reference 8

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This paper cites Bobenko and Ulrich Pinkall.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Bobenko and Ulrich Pinkall

Reference 9

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Observation a710cc7f-3a37-479f-b0a2-79e3d581e834 · outbound

This paper cites Bobenko and Yuri B.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Bobenko and Yuri B

Reference 10

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This paper cites Bobenko and Yuri B.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Bobenko and Yuri B

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:11.246588Z

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Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 12

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Observation 2708258b-ada1-4ba9-8713-e5b7293d8205 · outbound

This paper cites Lund, Toke B.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Lund, Toke B

Reference 13

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Observation d0445cdf-1917-4287-8ce5-63b8ebbf166f · outbound

This paper cites Nørbjerg.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Nørbjerg

Reference 14

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This paper cites Burstall and Susana D.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Burstall and Susana D

Reference 15

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Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 16

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Observation e264479e-cf08-474e-9331-4bfc89a6bac8 · outbound

This paper cites LMS Lecture Note Series.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves LMS Lecture Note Series

Reference 17

Resolution: malformed identifier; raw_fallback, observed 2026-08-10T16:17:11.236633Z

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Observation e17c5b7e-2873-4f9d-93ed-e12ba215039c · outbound

This paper cites Periodic discrete Darboux transforms.Differential Geometry and its Applications, 91:102065, 2023.doi:10.1016/j.difgeo.2023.102065.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Periodic discrete Darboux transforms.Differential Geometry and its Applications, 91:102065, 2023.doi:10.1016/j.difgeo.2023.102065

Reference 18

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Observation ca03a707-ebbf-4c17-a262-c656ca240897 · outbound

This paper cites Constrained elastic curves and surfaces with spherical curvature lines.Indiana University Mathematics Journal, (72(5):2059–2099), 2023.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Constrained elastic curves and surfaces with spherical curvature lines.Indiana University Mathematics Journal, (72(5):2059–2099), 2023

Reference 19

Resolution: verified exact; doi, observed 2026-08-10T16:17:10.545422Z

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Observation f70e3db6-a56f-4313-93d0-a906a9a5cd4b · outbound

This paper cites Discrete mKdV equation via Darboux transformation.Math- ematical Physics, Analysis and Geometry, 24, 09 2021.doi:10.1007/s11040-021-09398-y.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete mKdV equation via Darboux transformation.Math- ematical Physics, Analysis and Geometry, 24, 09 2021.doi:10.1007/s11040-021-09398-y

Reference 20

Resolution: verified exact; doi, observed 2026-08-10T16:17:10.532603Z

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Observation 42dfd543-a6d6-45c9-97b2-71c9e2dbbc1d · outbound

This paper cites Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio prob- lematis isoperimetrici lattissimo sensu accepti.Marcum-Michaelem Bousquet, 1744.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio prob- lematis isoperimetrici lattissimo sensu accepti.Marcum-Michaelem Bousquet, 1744

Reference 21

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Observation 7962e4ef-ebbe-46d9-a5da-774bd3046b61 · outbound

This paper cites Goldstein and Dean M.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Goldstein and Dean M

Reference 22

Resolution: verified exact; doi, observed 2026-08-10T16:17:10.519646Z

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Observation c4f8677a-15c9-40cd-9cba-d5cbe1784b71 · outbound

This paper cites On the zeros of polynomials over division rings.Transactions of the American Mathematical Society, 116:218–226, 1965.doi:10.1090/S0002-9947-1965-0195853-2.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves On the zeros of polynomials over division rings.Transactions of the American Mathematical Society, 116:218–226, 1965.doi:10.1090/S0002-9947-1965-0195853-2

Reference 23

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Observation 0f736515-27c6-45eb-8ff5-337fb8f25f9b · outbound

This paper cites The design space of plane elastic curves.ACM Transactions on Graphics, 40(4), 2021.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves The design space of plane elastic curves.ACM Transactions on Graphics, 40(4), 2021

Reference 24

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Observation d5516ddc-6fff-400f-807d-921e02caf08f · outbound

This paper cites Constrained Willmore tori and elastic curves in 2-dimensional space forms.Comm.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Constrained Willmore tori and elastic curves in 2-dimensional space forms.Comm

Reference 25

Resolution: verified exact; doi, observed 2026-08-10T16:17:10.495192Z

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Observation 049aa13b-440c-4aca-add6-4936ce62e729 · outbound

This paper cites Periodic discrete conformal maps.J.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Periodic discrete conformal maps.J

Reference 26

Resolution: verified exact; doi, observed 2026-08-10T16:17:10.481780Z

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Observation 652d8ca9-9291-4009-9f31-d2e9c33e6b84 · outbound

This paper cites Discrete Hashimoto surfaces and a doubly discrete smoke-ring flow.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete Hashimoto surfaces and a doubly discrete smoke-ring flow

Reference 27

Resolution: verified exact; doi, observed 2026-08-10T16:17:10.469226Z

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Observation 689f49e8-3cdb-46b3-b1b2-aaa9fdeaf26c · outbound

This paper cites Discrete differential geometry of curves and surfaces.Kyushu University Lecture Note Series Vol.18, 2009.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete differential geometry of curves and surfaces.Kyushu University Lecture Note Series Vol.18, 2009

Reference 28

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Observation a67713fd-825f-4f10-b221-32b7ed2b509c · outbound

This paper cites Discrete curves inCP1 and the Toda lattice.Studies in Applied Mathematics, 113(1):31–55, 2004.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete curves inCP1 and the Toda lattice.Studies in Applied Mathematics, 113(1):31–55, 2004

Reference 29

Resolution: verified exact; raw_fallback, observed 2026-08-10T16:17:10.921045Z

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Observation 2e942f70-60a8-4a17-a600-a3822e7d358b · outbound

This paper cites Skew parallelogram nets and universal factorization.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Skew parallelogram nets and universal factorization

Reference 30

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Observation 94b637d7-0242-41c0-89b1-38ce03b86f54 · outbound

This paper cites Isothermic nets with spherical parameter lines from discrete holomorphic maps.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Isothermic nets with spherical parameter lines from discrete holomorphic maps

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-10T16:17:10.441410Z

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Observation 6c1f627f-2b40-439b-a5e6-64c0b431e815 · outbound

This paper cites Discrete mKdV and discrete sine- Gordon flows on discrete space curves.Journal of Physics A: Mathematical and Theoretical, 47(23):235202, may 2014.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Discrete mKdV and discrete sine- Gordon flows on discrete space curves.Journal of Physics A: Mathematical and Theoretical, 47(23):235202, may 2014

Reference 32

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Observation 5bf5e375-a8cb-4036-9d44-11233dfe4f3e · outbound

This paper cites Polygon recutting as a cluster integrable system.Selecta Mathematica, 29(2):21, 2023.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Polygon recutting as a cluster integrable system.Selecta Mathematica, 29(2):21, 2023

Reference 33

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Observation 266b0f9e-7e75-4fdc-bb15-1558393460c1 · outbound

This paper cites Poisson geometry of the filament equation.Journal of Nonlinear Science, 1:71–93,.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Poisson geometry of the filament equation.Journal of Nonlinear Science, 1:71–93,

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:11.204504Z

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Observation 0f7e28e5-53ba-40d3-ba46-63fd583be40c · outbound

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Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 35

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Observation 0449a1c8-0a04-46d1-adff-59d700317fbb · outbound

This paper cites Scharler, and Hans-Peter Schröcker.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Scharler, and Hans-Peter Schröcker

Reference 36

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Observation e59c8d05-1ba0-4f3f-8c5c-a81151080e3b · outbound

This paper cites From Euler’s elastica to the mKdV hierarchy, through the Faber polynomials.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves From Euler’s elastica to the mKdV hierarchy, through the Faber polynomials

Reference 37

Resolution: verified exact; doi, observed 2026-08-10T16:17:10.382555Z

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Observation 97763187-54c4-4ee2-99cf-d88484a62a13 · outbound

This paper cites Equations in quaternions.The American Mathematical Monthly, 48(10):654–661, 1941.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Equations in quaternions.The American Mathematical Monthly, 48(10):654–661, 1941

Reference 38

Resolution: verified exact; raw_fallback, observed 2026-08-10T16:17:10.766187Z

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Observation 73e2d09b-d001-4cb6-aa2a-b7868458ce2d · outbound

This paper cites Compact Textbooks in Mathematics.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Compact Textbooks in Mathematics

Reference 39

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Observation 3bfeba17-5126-4fea-b4a9-8cebb7f52a57 · outbound

This paper cites A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow.Journal of Physics A: Mathematical and Theoretical, 40(42):12563,.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow.Journal of Physics A: Mathematical and Theoretical, 40(42):12563,

Reference 40

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Observation 1d5c972c-0a36-478b-abda-2d2045f3eb8d · outbound

This paper cites Springer-Verlag, 1970.doi:10.1007/978-3-642-86411-7.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Springer-Verlag, 1970.doi:10.1007/978-3-642-86411-7

Reference 41

Resolution: verified exact; doi, observed 2026-08-10T16:17:10.346377Z

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Observation 0e09e1d9-deeb-49a2-b7d4-48361f811b3e · outbound

This paper cites an unresolved cited work.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 42

Resolution: verified exact; doi, observed 2026-08-10T16:17:10.333046Z

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Observation 2e8fbc39-291c-4be3-a7e0-ad77ae20a456 · outbound

This paper cites On skew parallelogram nets, PhD thesis in preparation.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves On skew parallelogram nets, PhD thesis in preparation

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:11.182481Z

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Observation 746ed4ce-dca0-4de2-b4bc-46d1e6d052ea · outbound

This paper cites On the discrete bicycle transformation.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves On the discrete bicycle transformation

Reference 44

Resolution: verified exact; local_arxiv, observed 2026-08-10T16:17:10.320664Z

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Observation e890b598-253f-49e8-b472-eb53111e0223 · outbound

This paper cites Einfache elastische Kurven.Dissertation, TU Berlin, 1991.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Einfache elastische Kurven.Dissertation, TU Berlin, 1991

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:17:11.169924Z

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Observation e6c09177-efe9-41bf-999f-77be5d8285f8 · outbound

This paper cites Fairing of discrete planar curves by discrete Euler’s elasticae.JSIAM Letters, 11:73–76, 2019.doi:10.14495/jsiaml.11.73.

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Fairing of discrete planar curves by discrete Euler’s elasticae.JSIAM Letters, 11:73–76, 2019.doi:10.14495/jsiaml.11.73

Reference 46

Resolution: verified exact; doi, observed 2026-08-10T16:17:10.303436Z

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Observation ea7bddac-35bc-4126-a3e7-6cb2c07dedce · outbound

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Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 1991

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Discrete curve theory in space forms: planar elastic and area-constrained elastic curves Unresolved cited work

Reference 2007

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