A new proof of Huber's theorem on differential geometry in the large
Differential Geometry
2022-12-16 v3 Complex Variables
Abstract
In this paper we give a new, and shorter, proof of Huber's theorem which affirms that for a connected open Riemann surface endowed with a complete conformal Riemannian metric, if the negative part of its Gaussian curvature has finite mass, then the Riemann surface is homeomorphic to the interior of a compact surface with boundary, and thus it has finite topological type. We will also show that such Riemann surface is parabolic.
Keywords
Cite
@article{arxiv.2201.11348,
title = {A new proof of Huber's theorem on differential geometry in the large},
author = {Chen Zhou},
journal= {arXiv preprint arXiv:2201.11348},
year = {2022}
}