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Quantitative Thomas–Yau uniqueness

Yang Li
Geometry & Topology 29 (2025) 2251–2268
DOI: 10.2140/gt.2025.29.2251
Abstract

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.

Keywords
special Lagrangian, Thomas–Yau uniqueness theorem, geometric measure theory, Floer cohomology
Mathematical Subject Classification
Primary: 53C38, 53D12, 57R58
References
Publication
Received: 24 September 2022
Revised: 29 October 2024
Accepted: 30 November 2024
Published: 14 August 2025
Proposed: Richard P Thomas
Seconded: Mark Gross, Jim Bryan
Authors
Yang Li
Department of Pure Mathematics and Mathematical Statistics
Cambridge University
Cambridge
United Kingdom
© 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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