Abstract:We establish local variational characterizations of non-degenerate free-boundary minimal hypersurfaces in compact Riemannian manifolds with boundary.
For a two-sided strictly stable hypersurface, we show that it is the unique mass minimizer in its relative homology class, both in a small tubular and flat-neighborhood. As an application, for generic metrics in dimensions $3\le n+1\le 7$, we show that the first free-boundary width is realized by a multiplicity-one hypersurface of Morse index one.
For an orientable non-degenerate free-boundary hypersurface of Morse index $k>0$, we construct a canonical local $k$-parameter family and obtain a local min--max characterization.
From: Hangyue Zhu [view email]
[v1]
Mon, 25 May 2026 08:34:58 UTC (38 KB)
[v2]
Wed, 29 Jul 2026 10:20:23 UTC (331 KB)
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