An interior curvature bound for hypersurfaces of prescribed k-th mean curvature

John Urbas

doi:10.1515/crll.2000.016

An interior curvature bound for hypersurfaces of prescribed k-th mean curvature

John Urbas^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

We derive an interior curvature bound for k-admissible hypersurfaces in ℝⁿ⁺¹ of prescribed k-th mean curvature in terms of the L^p norm of the mean curvature for some p > kn/2. Examples show that in the cases k ≧ 3 such a bound is generally false if p is not sufficiently large.

Original language	English
Pages (from-to)	41-57
Number of pages	17
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	519
DOIs	https://doi.org/10.1515/crll.2000.016
Publication status	Published - 2000

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10.1515/crll.2000.016

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abstract = "We derive an interior curvature bound for k-admissible hypersurfaces in ℝn+1 of prescribed k-th mean curvature in terms of the Lp norm of the mean curvature for some p > kn/2. Examples show that in the cases k ≧ 3 such a bound is generally false if p is not sufficiently large.",

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AB - We derive an interior curvature bound for k-admissible hypersurfaces in ℝn+1 of prescribed k-th mean curvature in terms of the Lp norm of the mean curvature for some p > kn/2. Examples show that in the cases k ≧ 3 such a bound is generally false if p is not sufficiently large.

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JO - Journal fur die Reine und Angewandte Mathematik

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ER -

An interior curvature bound for hypersurfaces of prescribed k-th mean curvature

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