Submanifolds with nonpositive extrinsic curvature

We prove that complete submanifolds, on which the Omori-Yau weak maximum principle for the Hessian holds, with low codimension and bounded by cylinders of small radius must have points rich in large positive extrinsic curvature. The lower the codimension is, the richer such points are. The smaller t...

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Published in:arXiv.org 2015-07
Main Authors: Canevari, Samuel, Guilherme Machado de Freitas, Manfio, Fernando
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Language:English
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Curvature
Cylinders
Manifolds (mathematics)
Maximum principle
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Guilherme Machado de Freitas
Manfio, Fernando
description We prove that complete submanifolds, on which the Omori-Yau weak maximum principle for the Hessian holds, with low codimension and bounded by cylinders of small radius must have points rich in large positive extrinsic curvature. The lower the codimension is, the richer such points are. The smaller the radius is, the larger such curvatures are. This work unifies and generalizes several previous results on submanifolds with nonpositive extrinsic curvature.
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subjects Curvature
Cylinders
Manifolds (mathematics)
Maximum principle
title Submanifolds with nonpositive extrinsic curvature
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