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PreprintCC BY 4.0arXiv

Topology and Dirichlet spectrum of free boundary minimal and CMC surfaces

  • Alcides de Carvalho
  • Roney Santos
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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.

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Cite

BibTeXRIS
BibTeX
@misc{carvalho2026topology,
  title = {{Topology and Dirichlet spectrum of free boundary minimal and CMC surfaces}},
  author = {Alcides de Carvalho and Roney Santos},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31304},
  eprint = {2609.31304},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31304},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Topology and Dirichlet spectrum of free boundary minimal and CMC surfaces
AU  - Alcides de Carvalho
AU  - Roney Santos
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31304
UR  - https://arxiv.org/abs/2609.31304
AB  - 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.
ER  -