Geodesic
Quantitative Thomas–Yau uniqueness
Li, Yang1
1Department of Pure Mathematics and Mathematical Statistics, Cambridge University, Cambridge, United Kingdom
Geometry & topology, Tome 29 (2025) no. 5, pp. 2251-2268
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

Under Floer-theoretic conditions, we obtain quantitative estimates on the closeness (Hausdorff distance, flat norm and F-metric) between two Lagrangians, depending on the smallness of Lagrangian angles. Some applications include a strong–weak uniqueness theorem for special Lagrangians, and a characterization of varifold convergence to special Lagrangians in terms of Lagrangian angles.

DOI : 10.2140/gt.2025.29.2251
Keywords: special Lagrangian, Thomas–Yau uniqueness theorem, geometric measure theory, Floer cohomology

Li, Yang  1

1 Department of Pure Mathematics and Mathematical Statistics, Cambridge University, Cambridge, United Kingdom 
@article{10_2140_gt_2025_29_2251,
     author = {Li, Yang},
     title = {Quantitative {Thomas{\textendash}Yau} uniqueness},
     journal = {Geometry & topology},
     pages = {2251--2268},
     year = {2025},
     volume = {29},
     number = {5},
     doi = {10.2140/gt.2025.29.2251},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2025.29.2251/}
}
TY  - JOUR
AU  - Li, Yang
TI  - Quantitative Thomas–Yau uniqueness
JO  - Geometry & topology
PY  - 2025
SP  - 2251
EP  - 2268
VL  - 29
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2025.29.2251/
DO  - 10.2140/gt.2025.29.2251
ID  - 10_2140_gt_2025_29_2251
ER  - 
%0 Journal Article
%A Li, Yang
%T Quantitative Thomas–Yau uniqueness
%J Geometry & topology
%D 2025
%P 2251-2268
%V 29
%N 5
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2025.29.2251/
%R 10.2140/gt.2025.29.2251
%F 10_2140_gt_2025_29_2251
Li, Yang. Quantitative Thomas–Yau uniqueness. Geometry & topology, Tome 29 (2025) no. 5, pp. 2251-2268. doi: 10.2140/gt.2025.29.2251

[1] M Abouzaid, Y Imagi, Nearby special Lagrangians, preprint (2021)

[2] M Akaho, D Joyce, Immersed Lagrangian Floer theory, J. Differential Geom. 86 (2010) 381

[3] F Almgren, Optimal isoperimetric inequalities, Indiana Univ. Math. J. 35 (1986) 451 | DOI

[4] V I Arnol’D, Dynamics of complexity of intersections, Bol. Soc. Brasil. Mat. 21 (1990) 1 | DOI

[5] D Auroux, A beginner’s introduction to Fukaya categories, from: "Contact and symplectic topology" (editors F Bourgeois, V Colin, A Stipsicz), Bolyai Soc. Math. Stud. 26, János Bolyai Math. Soc. (2014) 85 | DOI

[6] Y Imagi, A uniqueness theorem for gluing calibrated submanifolds, Comm. Anal. Geom. 23 (2015) 691 | DOI

[7] Y Imagi, D Joyce, J Oliveira Dos Santos, Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in Cm, Duke Math. J. 165 (2016) 847 | DOI

[8] D Joyce, Conjectures on Bridgeland stability for Fukaya categories of Calabi–Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow, EMS Surv. Math. Sci. 2 (2015) 1 | DOI

[9] Y Li, Thomas–Yau conjecture and holomorphic curves, EMS Surv. Math. Sci. (2025) | DOI

[10] A Neves, Recent progress on singularities of Lagrangian mean curvature flow, from: "Surveys in geometric analysis and relativity" (editors H L Bray, W P Minicozzi), Adv. Lect. Math. 20, International (2011) 413

[11] P Seidel, Categorical dynamics, lecture notes (2012)

[12] R P Thomas, S T Yau, Special Lagrangians, stable bundles and mean curvature flow, Comm. Anal. Geom. 10 (2002) 1075 | DOI

Cité par Sources :