Compactness for minimal surfaces with injectivity radius bounded from below

Luan de Figueiredo; Rosivaldo Gonçalves

Compactness for minimal surfaces with injectivity radius bounded from below

微分几何 2026-06-27 v1

作者: Luan de Figueiredo , Rosivaldo Gonçalves

摘要

We prove a compactness theorem for the space of closed embedded minimal surfaces with area bounded from above and injectivity radius bounded from below in a closed Riemannian $3$ -manifold. This result is a variant of the Choi--Schoen compactness theorem in which the genus bound is replaced by a lower bound on the injectivity radius of the surface.

引用

@article{arxiv.2606.29045,
  title  = {Compactness for minimal surfaces with injectivity radius bounded from below},
  author = {Luan de Figueiredo and Rosivaldo Gonçalves},
  journal= {arXiv preprint arXiv:2606.29045},
  year   = {2026}
}