{"total":17,"items":[{"citing_arxiv_id":"2606.06619","ref_index":54,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"On the structure of complete $G_2$-solitons","primary_cat":"math.DG","submitted_at":"2026-06-04T18:11:34+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Proves compactness and convergence theorems for complete gradient G2-solitons under scalar curvature lower bounds and potential growth conditions.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.23679","ref_index":4,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Geometrisation of 3-manifolds","primary_cat":"math.GT","submitted_at":"2026-05-22T14:27:32+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":0.0,"formal_verification":"none","one_line_summary":"An overview of the geometrisation theorem for 3-manifolds that explains its content and effects in various situations.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.14572","ref_index":14,"ref_count":2,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Modifications of CMB Temperature and Polarization Quadrupole Signals in Thurston Spacetimes","primary_cat":"gr-qc","submitted_at":"2026-05-14T08:43:08+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"The authors introduce Thurston spacetimes as cosmological backgrounds, solve transfer equations for temperature and polarization patterns, and analyze symmetries in Stokes parameters to attempt isolation of individual geometries.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.05599","ref_index":1,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Notes on harmonic-Ricci flow on surface","primary_cat":"math.DG","submitted_at":"2026-05-07T02:35:20+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":2.0,"formal_verification":"none","one_line_summary":"Establishes several evolution formulas for functionals along the harmonic-Ricci flow on surfaces with boundary.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.02279","ref_index":14,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Foundations of Riemannian Geometry for Riemannian Optimization: A Monograph with Detailed Derivations","primary_cat":"math.DG","submitted_at":"2026-05-04T07:11:11+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":2.0,"formal_verification":"none","one_line_summary":"The monograph organizes and derives classical Riemannian geometry structures explicitly in coordinate and matrix form for direct use in optimization algorithms on nonlinear manifolds.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.20761","ref_index":40,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Geometric Renyi Differential Privacy: Ricci Curvature Characterized by Heat Diffusion Mechanisms","primary_cat":"stat.ML","submitted_at":"2026-04-22T16:48:55+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Renyi differential privacy for manifold-valued data is characterized via dimension-free Harnack inequalities and governed by Ricci curvature, with heat diffusion and Langevin mechanisms plus application to private Frechet mean estimation.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.18678","ref_index":34,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"The perturbative Ricci flow in gravity","primary_cat":"hep-th","submitted_at":"2026-04-20T18:00:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"A perturbative Ricci-flow formulation in gravity yields a renormalization scheme for Newton's constant that exhibits a non-Gaussian fixed point at two-loop order.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Ninomiya, Nucl. Phys. B404, 684 (1993), arXiv:hep-th/9303123. [32] R. Martini, G. P. Vacca, and O. Zanusso, Perturba- tive Approaches to Nonperturbative Quantum Grav- ity, inHandbook of Quantum Gravity, edited by C. Bambi, L. Modesto, and I. Shapiro (2024) pp. 1-46, arXiv:2210.13910 [hep-th]. [33] R. S. Hamilton, Journal of Differential Geometry17, 255 (1982). [34] G. Perelman, preprint (2003), arXiv:math/0307245. [35] G. Perelman, preprint (2006), arXiv:math/0211159. [36] G. Perelman, preprint (2006), arXiv:math/0303109. [37] M. L¨ uscher, JHEP08, 071, [Erratum: JHEP 03, 092 (2014)], arXiv:1006.4518 [hep-lat]. [38] M. L¨ uscher and P. Weisz, JHEP02, 051, arXiv:1101.0963 [hep-th]. [39] M. L¨ uscher, JHEP04, 123, arXiv:1302."},{"citing_arxiv_id":"2604.10007","ref_index":21,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"On weak formulations of (super) Ricci flows","primary_cat":"math.DG","submitted_at":"2026-04-11T03:31:29+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Smooth compact Ricci flows are characterized weakly solely via metrics and measures by defining super Ricci flows and adding a saturation condition to recover equality.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.06344","ref_index":8,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"On the Chern-Ricci form of a twisted almost K\\\"{a}hler structure","primary_cat":"math.DG","submitted_at":"2026-04-07T18:25:39+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"An explicit formula is given for the local connection 1-form α on the anti-canonical bundle of a twisted almost Kähler structure, yielding the Chern-Ricci form as ρ = -dα.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.02632","ref_index":27,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"The Calabi flow with prescribed curvature on finite graphs","primary_cat":"math.DG","submitted_at":"2026-04-03T01:55:03+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The Calabi flow on finite graphs converges globally if and only if a weight function exists realizing the prescribed curvature, with convergence for constant curvature under topological conditions.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Adv. Math. 356, 106759, 45, 2019. [24] Y . Ollivier.Ricci curvature of markov chains on metric spaces. J. Funct. Anal. 256(3): 810-864, 2007. [25] G. Perelman.The entropy formula for the Ricci flow and its geometric applications. aarXiv:math/0211159[math.DG]. [26] G. Perelman.Ricci flow with surgery on three-manifolds. arXiv:math/0303109[math.DG]. [27] G. Perelman.Finite extinction time for the solutions to the Ricci flow on certain threep-manifolds. arXiv:math/0307245[math.DG]. [28] L.S. Pontryagin.Ordinary differential equations, Addison-Wesley Publishing Company Inc., Reading, 1962. [29] W. Thurston,Geometry and topology of3-manifolds, Princeton lecture notes 1976, http://www.msri.org/publications/books/gt3m."},{"citing_arxiv_id":"2603.10479","ref_index":28,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"The Ricci flow with prescribed curvature on graphs","primary_cat":"math.DG","submitted_at":"2026-03-11T07:07:52+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A discrete Ricci flow on graphs converges exponentially to prescribed Lin-Lu-Yau curvatures iff attainable, with an explicit max-edge-density condition for constant curvature on girth-at-least-6 graphs.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2512.07708","ref_index":46,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Bianchi cosmologies in a Thurston-based theory of gravity","primary_cat":"gr-qc","submitted_at":"2025-12-08T16:54:25+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"In a Thurston-geometry-dependent gravity theory, non-tilted BKS cosmologies admit shear-free perfect-fluid and static vacuum solutions for all topologies, isotropize under positive Lambda except for some Bianchi II cases, and never recollapse when the weak energy condition holds.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2511.20568","ref_index":19,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"On the rigidity of special and exceptional geometries with torsion a closed $3$-form","primary_cat":"math.DG","submitted_at":"2025-11-25T18:04:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2510.20320","ref_index":11,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow","primary_cat":"math.DG","submitted_at":"2025-10-23T08:14:20+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Establishes a Lojasiewicz inequality for pointed W-entropy near cylindrical singularities in Ricci flow and applies it to prove strong uniqueness of the cylindrical tangent flow at the first singular time under a fixed gauge.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2509.16553","ref_index":18,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Cosmological viability of anisotropic inflation in Thurston spacetimes","primary_cat":"gr-qc","submitted_at":"2025-09-20T06:44:08+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Inflationary models on Thurston geometries admit a stable anisotropic fixed point triggered by eccentricity-induced vector field coupling to the inflaton.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2411.19400","ref_index":25,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Exotic aspherical 4-manifolds","primary_cat":"math.GT","submitted_at":"2024-11-28T22:30:26+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"Constructs closed aspherical 4-manifolds that are homeomorphic but not diffeomorphic, providing counterexamples to the smooth Borel conjecture in dimension 4.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2302.04964","ref_index":53,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Ancient Ricci flows of bounded girth","primary_cat":"math.DG","submitted_at":"2023-02-09T22:42:36+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Constructs O(2)×O(n-1)-invariant ancient Ricci flows with positive curvature operator and bounded girth for n≥3 and determines their backward asymptotic limits.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}