Year: 2026
Type: preprint
Abstract: We find bounds for the genus and for the number of boundary components of a surface that is either index one as a free boundary minimal surface or stable as a free boundary constant mean curvature surface in a Riemannian three-manifold with convex boundary and non-negative Ricci curvature, provided the first Dirichlet eigenvalue of its Jacobi operator is non-negative. As an application, we establish strong topological restrictions on such surfaces in compact strictly convex domains of three-dimensional normal homogeneous spaces.
Source: arXiv (Cornell University)
Authors: de Carvalho, Alcides, Santos, Roney
Institutions: Universidade Federal de Pernambuco, King's College London
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214635507