A new proof of Huber's theorem on differential geometry in the large

Chen Zhou

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arXiv · 2201.11348

A new proof of Huber's theorem on differential geometry in the large

Chen Zhou

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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.

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Chen Zhou. 2022-01-27. A new proof of Huber's theorem on differential geometry in the large. https://arxiv.org/abs/2201.11348

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