Submanifolds with nonpositive extrinsic curvature
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2015
- DOI:
- 10.48550/arXiv.1507.02523
- arXiv:
- arXiv:1507.02523
- Bibcode:
- 2015arXiv150702523C
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- 20 pages. arXiv admin note: text overlap with arXiv:0907.5025 by other authors