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arXiv · 1512.04760

Complete hypersurfaces in Euclidean spaces with strong finite total curvature

Manfredo do Carmo·Maria Fernanda Elbert
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Abstract

We prove that strong finite total curvature complete hypersurfaces of (n+1)-euclidean space are proper and diffeomorphic to a compact manifold minus finitely many points. With an additional condition, we also prove that the Gauss map of such hypersurfaces extends continuously to the punctures.

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Manfredo do Carmo, Maria Fernanda Elbert. 2015-12-15. Complete hypersurfaces in Euclidean spaces with strong finite total curvature. https://arxiv.org/abs/1512.04760

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