Minimal surfaces of finite total curvature in \mathbbM² × ℝ

2019/01/23 by Rafael Ponte, Ponte, Rafael
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1901.08046

openalex publication_date 2019/01/23 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28

Abstract

The goal of this article is to study minimal surfaces in \mathbbM² × ℝ having finite total curvature, where \mathbbM² 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 2π.

Citations

• Differential equations on riemannian manifolds and their geometric applications

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