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On the stability of free boundary minimal submanifolds in conformal domains

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arxiv 2409.03943 v1 pith:GZOHXZ5W submitted 2024-09-05 math.DG

Alcides de Carvalho , Roney Santos , Federico Trinca This is my paper · ORCID
classification math.DG
keywords boundaryconvexconformalcurvaturesfreeminimalsectionalstrictly
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abstract

Given a $n$-dimensional Riemannian manifold with non-negative sectional curvatures and convex boundary, that is conformal to an Euclidean convex bounded domain, we show that it does not contain any compact stable free boundary minimal submanifold of dimension $2\leq k\leq n-2$, provided that either the boundary is strictly convex with respect to any of the two metrics or the sectional curvatures are strictly positive.

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