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arXiv · 1405.0851

Complete Surfaces with Ends of Non Positive Curvature

José A. Gálvez·Antonio Martínez·José L. Teruel
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Abstract

In this paper we extend Efimov's Theorem by proving that any complete surface in $\mathbb{R}^3$ with Gauss curvature bounded above by a negative constant outside a compact set has finite total curvature, finite area and is properly immersed. Moreover, its ends must be asymptotic to half-lines. We also give a partial solution to Milnor's conjecture by studying isometric immersions in a space form of complete surfaces which satisfy that outside a compact set they have non positive Gauss curvature and the square of a principal curvature function is bounded from below by a positive constant.

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José A. Gálvez, Antonio Martínez, José L. Teruel. 2014-05-05. Complete Surfaces with Ends of Non Positive Curvature. https://arxiv.org/abs/1405.0851

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