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

Eduardo Longa

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

Differential Geometry 2021-04-13 v1

Authors: Eduardo Longa

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.

Keywords

capillary minimal surface riemannian 3-manifold local rigidity low index mean convex boundary genus bound area bound

Cite

@article{arxiv.2104.05148,
  title  = {Low index capillary minimal surfaces in Riemannian $3$-manifolds},
  author = {Eduardo Longa},
  journal= {arXiv preprint arXiv:2104.05148},
  year   = {2021}
}

Comments

16 pages, 2 figures

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