Unknottedness of free boundary minimal surfaces and self-shrinkers
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526_2025_Article_3082.pdf
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Author(s)
Chu, Sabine
Franz, Giada
Date Issued
September 8, 2025
Journal
Calculus of Variations and Partial Differential Equations
Publisher
Springer Berlin Heidelberg
Citation
Chu, S., Franz, G. Unknottedness of free boundary minimal surfaces and self-shrinkers. Calc. Var. 64, 237 (2025).
Version
Final published version
Abstract
We study unknottedness for free boundary minimal surfaces in a three-dimensional Riemannian manifold with nonnegative Ricci curvature and strictly convex boundary, and for self-shrinkers in the three-dimensional Euclidean space. For doing so, we introduce the concepts of boundary graph for free boundary minimal surfaces and of graph at infinity for self-shrinkers. We prove that these surfaces are unknotted in the sense that any two such surfaces with isomorphic boundary graph or graph at infinity are smoothly isotopic.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s00526-025-03082-7
