Paper Citation Record · LEDGER

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds

As of 19 August 2026, this Paper Citation Record lists 64 of 64 outbound references and 2 inbound Pith citation observations for arXiv:2412.12889.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.12889 v2

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Reference resolution

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Outbound references

Observation d8aab363-6642-4ae9-b7f4-6e6125c1795e · outbound

This paper cites an unresolved cited work.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Unresolved cited work

Reference 1

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Observation ebdce2fe-6c5d-4802-afa3-e1443d4ea75b · outbound

This paper cites Alberti, S.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Alberti, S

Reference 2

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Observation dea31ae6-e2ca-4298-b739-829df1490ccf · outbound

This paper cites Almgren, W.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Almgren, W

Reference 3

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Observation 971c91bd-bd25-4dd9-9e61-8a2b077ea251 · outbound

This paper cites Bernot, V.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Bernot, V

Reference 4

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This paper cites Bethuel, A characterization of maps in H 1(B3,S 2) which can be approximated by smooth maps, Ann.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Bethuel, A characterization of maps in H 1(B3,S 2) which can be approximated by smooth maps, Ann

Reference 5

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This paper cites Bethuel,The approximation problem for Sobolev maps between two manifolds, Acta Math.167 (1991), no.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Bethuel,The approximation problem for Sobolev maps between two manifolds, Acta Math.167 (1991), no

Reference 6

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Observation f9ce9d4a-d526-4a39-b6f0-56db09ddf6fa · outbound

This paper cites Fixed Point Theory Appl.15 (2014), no.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Fixed Point Theory Appl.15 (2014), no

Reference 7

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This paper cites Math.219 (2020), no.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Math.219 (2020), no

Reference 8

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This paper cites Bethuel and D.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Bethuel and D

Reference 9

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This paper cites Bethuel and F.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Bethuel and F

Reference 10

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This paper cites Bethuel and X.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Bethuel and X

Reference 11

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Observation dc891a9d-ab71-4e89-a4f9-a96410e1297f · outbound

This paper cites Bourgain, H.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Bourgain, H

Reference 12

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This paper cites Bousquet, A.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Bousquet, A

Reference 13

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Unresolved cited work

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Unresolved cited work

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This paper cites Brezis and J.-M.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Brezis and J.-M

Reference 16

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Brezis, J.-M

Reference 17

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This paper cites Brezis and P.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Brezis and P

Reference 18

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Unresolved cited work

Reference 19

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Brezis and L

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Canevari and G

Reference 21

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Da Lio and T

Reference 22

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Deny and J.-L

Reference 23

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This paper cites Detaille, A complete answer to the strong density problem in Sobolev spaces with values into compact manifolds(2023), available athttps://arxiv.org/abs/2305.12589.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Detaille, A complete answer to the strong density problem in Sobolev spaces with values into compact manifolds(2023), available athttps://arxiv.org/abs/2305.12589

Reference 24

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Eells and L

Reference 25

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This paper cites Eells and J.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Eells and J

Reference 26

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Unresolved cited work

Reference 27

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Observation 1cb14286-3f64-4be9-a67e-bbfc54837b32 · outbound

This paper cites Gastel,Partial regularity of polyharmonic maps to targets of sufficiently simple topology, Z.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Gastel,Partial regularity of polyharmonic maps to targets of sufficiently simple topology, Z

Reference 28

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Observation 8a435490-ce32-46b2-8bba-f193f4328a86 · outbound

This paper cites Giaquinta, G.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Giaquinta, G

Reference 29

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Observation 4a14e9b2-4603-47f7-88ca-d660b12fefdd · outbound

This paper cites Hajłasz, Approximation of Sobolev mappings, Nonlinear Anal.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Hajłasz, Approximation of Sobolev mappings, Nonlinear Anal

Reference 30

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Observation ed6045e0-95f2-493a-84d6-bb11d09d9635 · outbound

This paper cites Hang,Density problems forW 1,1(M,N ), Comm.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Hang,Density problems forW 1,1(M,N ), Comm

Reference 31

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Hang and F

Reference 32

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds III, Comm

Reference 33

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Hardt and T

Reference 34

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds 200 (2008), no

Reference 35

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Hardt and T

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This paper cites Hatcher,Algebraic topology, Cambridge University Press, Cambridge, 2002.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Hatcher,Algebraic topology, Cambridge University Press, Cambridge, 2002

Reference 37

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Hélein and J

Reference 38

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Huang, Y

Reference 39

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Unresolved cited work

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This paper cites Jost,Harmonic maps between surfaces, Lecture Notes in Mathematics, vol.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Jost,Harmonic maps between surfaces, Lecture Notes in Mathematics, vol

Reference 41

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Unresolved cited work

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Mironescu and J

Reference 45

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Monteil and J

Reference 47

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Nakauchi and S

Reference 48

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Nash,C 1 isometric imbeddings, Ann

Reference 49

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Reference 50

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Reference 52

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Observation d2644f96-8e8e-4b03-a3e4-4106bdeb4395 · outbound

This paper cites Rivière,Minimizing fibrations andp-harmonic maps in homotopy classes fromS3 into S2, Comm.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Rivière,Minimizing fibrations andp-harmonic maps in homotopy classes fromS3 into S2, Comm

Reference 53

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This paper cites Runst,Mapping properties of nonlinear operators in spaces of Triebel-Lizorkin and Besov type, Anal.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Runst,Mapping properties of nonlinear operators in spaces of Triebel-Lizorkin and Besov type, Anal

Reference 54

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Observation aa6df02c-c96e-4ebe-ac9e-ef6272c8bd35 · outbound

This paper cites Sacks and K.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Sacks and K

Reference 55

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This paper cites Sandier,Lower bounds for the energy of unit vector fields and applications, J.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Sandier,Lower bounds for the energy of unit vector fields and applications, J

Reference 56

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Observation 28649317-cda4-4d88-9cdc-965715c3043e · outbound

This paper cites Sandier and S.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Sandier and S

Reference 57

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Observation 5fb1e8b0-66c6-4a00-b835-0fc6828bac4e · outbound

This paper cites Schoen and K.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Schoen and K

Reference 58

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Observation d2b5c4bd-1acd-4a18-b92a-41df0df2e55b · outbound

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Unresolved cited work

Reference 59

Resolution: malformed identifier; no resolver link, observed 2026-08-11T13:49:10.862926Z

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Observation 72261ee7-3ebc-4a59-955f-021ace6be6ca · outbound

This paper cites Schikorra and J.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Schikorra and J

Reference 60

Resolution: verified exact; doi, observed 2026-08-11T13:49:11.017576Z

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Observation 15374271-b9e3-4bd4-802c-31dad8269c89 · outbound

This paper cites Urakawa,Geometry of biharmonic mappings: Differential geometry of variational methods, World Scientific, Hackensack, N.J., 2019, doi:10.1142/10886.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Urakawa,Geometry of biharmonic mappings: Differential geometry of variational methods, World Scientific, Hackensack, N.J., 2019, doi:10.1142/10886

Reference 61

Resolution: malformed identifier; doi_truncated, observed 2026-08-11T13:49:10.999073Z

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Observation a98b1982-e175-427d-a783-ec681a944230 · outbound

This paper cites White,Homotopy classes in Sobolev spaces and the existence of energy minimizing maps, Acta Math.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds White,Homotopy classes in Sobolev spaces and the existence of energy minimizing maps, Acta Math

Reference 62

Resolution: verified exact; doi, observed 2026-08-11T13:49:10.978559Z

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Observation 99ee0de3-cf9c-498d-862a-3171dd2c42df · outbound

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Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Unresolved cited work

Reference 63

Resolution: verified exact; doi, observed 2026-08-11T13:49:10.958744Z

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Observation ec26f096-b7c3-4b1d-90a0-49269a483858 · outbound

This paper cites an unresolved cited work.

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds Unresolved cited work

Reference 64

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Pith citing papers

Observation 135ce5e5-00f2-4fda-a7cd-2a3029c20c3b · inbound

Generic topological screening and approximation of Sobolev maps cites this paper.

Generic topological screening and approximation of Sobolev maps Analytical obstructions to the weak approximation of Sobolev mappings into manifolds

Reference 36

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Observation aece2c29-9744-4107-bb2d-de85c7a77a6e · inbound

Topological singular set of manifold-valued maps weakly approximable by smooth maps cites this paper.

Topological singular set of manifold-valued maps weakly approximable by smooth maps Analytical obstructions to the weak approximation of Sobolev mappings into manifolds

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-06-29T09:53:17.561023Z

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