Manfredo do Carmo, Maria Fernanda Elbert
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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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.
Key concepts: Mathematics, Diffeomorphism, Euclidean space, Curvature, Euclidean geometry, Manifold (fluid mechanics), Pure mathematics, Space (punctuation)