Minimal surfaces of finite total curvature in $\mathbb{M}^2 \times \mathbb{R}$

Rafael Ponte

Minimal surfaces of finite total curvature in $\mathbb{M}^2 \times \mathbb{R}$

Differential Geometry 2019-01-24 v1

Authors: Rafael Ponte

Abstract

The goal of this article is to study minimal surfaces in $\mathbb{M}^2 \times \mathbb{R}$ having finite total curvature, where $\mathbb{M}^2$ is a Hadamard manifold. The main result gives a formula to compute the total curvature in terms of topological, geometrical and conformal data of the minimal surface. In particular, we prove the total curvature is an integral multiple of $2\pi$ .

Keywords

minimal surfaces finite total curvature Hadamard manifold conformal data topological formula

Cite

@article{arxiv.1901.08046,
  title  = {Minimal surfaces of finite total curvature in $\mathbb{M}^2 \times \mathbb{R}$},
  author = {Rafael Ponte},
  journal= {arXiv preprint arXiv:1901.08046},
  year   = {2019}
}

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