论保形域中自由边界最小子曼形体的稳定性

arXiv - MATH - Differential Geometry Pub Date : 2024-09-05 DOI:arxiv-2409.03943

Alcides de Carvalho, Roney Santos, Federico Trinca

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引用次数: 0

摘要

给定一个具有非负截面曲率和凸边界的 $n$ 维黎曼流形，它与欧几里得凸界域保角，我们证明它不包含任何维数为 $2\leq k\leq n-2$ 的紧凑稳定自由边界最小子流形，条件是边界相对于两个度量中的任何一个是严格凸的，或者截面曲率是严格正的。

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On the stability of free boundary minimal submanifolds in conformal domains

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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arXiv - MATH - Differential Geometry

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