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arXiv · 2301.13130

Stability of Convex Disks

Hunter Stufflebeam
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Abstract

We prove that topological disks with positive curvature and strictly convex boundary of large length are close to round spherical caps of constant boundary curvature in the Gromov-Hausdorff sense. This proves stability for a theorem of F. Hang and X. Wang, and can be viewed as an affirmative answer to a convex stability version of the Min-Oo Conjecture in dimension two. As an intermediate step, we obtain a compactness result for a Liouville-type PDE problem.

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Hunter Stufflebeam. 2023-01-30. Stability of Convex Disks. https://doi.org/10.1007/s00526-023-02582-8

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