Low index capillary minimal surfaces in Riemannian $3$-manifolds

Eduardo Longa

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arXiv · 2104.05148

Low index capillary minimal surfaces in Riemannian $3$-manifolds

Eduardo Longa

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Abstract

We prove a local rigidity result for infinitesimally rigid capillary surfaces in some Riemannian $3$-manifolds with mean convex boundary. We also derive bounds on the genus, number of boundary components and area of any compact two-sided capillary minimal surface with low index under certain assumptions on the curvature of the ambient manifold and of its boundary.

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Eduardo Longa. 2021-04-12. Low index capillary minimal surfaces in Riemannian $3$-manifolds. https://arxiv.org/abs/2104.05148

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