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- W4383987305 abstract "In this paper we prove a rigidity statement for free boundary minimal surfaces produced via min-max methods. More precisely, we prove that for any Riemannian metric $g$ on the 3-ball $B$ with non-negative Ricci curvature and $mathrm{II}_{partial B}ge g_{|partial B}$, there exists a free boundary minimal disk $Delta$ of least area among all free boundary minimal disks in $(B,g)$. Moreover, the area of any such $Delta$ equals to the width of $(B,g)$, $Delta$ has index one, and the length of $partialDelta$ is bounded from above by $2pi$. Furthermore, the length of $partialDelta$ equals to $2pi$ if and only if $(B,g)$ is isometric to the Euclidean unit ball. This is related to a rigidity result obtained by F.C. Marques and A. Neves in the closed case. The proof uses a rigidity statement concerning half-balls with non-negative Ricci curvature which is true in any dimension." @default.
- W4383987305 created "2023-07-12" @default.
- W4383987305 creator A5019972470 @default.
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- W4383987305 date "2023-07-07" @default.
- W4383987305 modified "2023-09-23" @default.
- W4383987305 title "Rigidity of min-max minimal disks in $3$-balls with non-negative Ricci curvature" @default.
- W4383987305 doi "https://doi.org/10.48550/arxiv.2307.03624" @default.
- W4383987305 hasPublicationYear "2023" @default.
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