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

DOI10.1007/S10711-023-00769-ZarXiv2201.11348MaRDI QIDQ6389338

Publication date: 27 January 2022

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.

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Riemann surfaces (30F99)

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