Monotonicity formulae and curvature equations

John Urbas

doi:10.1515/crll.2003.031

Monotonicity formulae and curvature equations

John Urbas^*

^*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

We derive local integral estimates and monotonicity formulae for certain curvature quantities related to hypersurfaces of prescribed k-th mean curvature. We use these to improve interior curvature bounds established in previous work, and to derive a local Hölder gradient estimate for admissible solutions of the equation of prescribed scalar curvature.

Original language	English
Pages (from-to)	199-218
Number of pages	20
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	557
DOIs	https://doi.org/10.1515/crll.2003.031
Publication status	Published - 2003

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10.1515/crll.2003.031

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title = "Monotonicity formulae and curvature equations",

abstract = "We derive local integral estimates and monotonicity formulae for certain curvature quantities related to hypersurfaces of prescribed k-th mean curvature. We use these to improve interior curvature bounds established in previous work, and to derive a local H{\"o}lder gradient estimate for admissible solutions of the equation of prescribed scalar curvature.",

author = "John Urbas",

year = "2003",

doi = "10.1515/crll.2003.031",

language = "English",

pages = "199--218",

journal = "Journal fur die Reine und Angewandte Mathematik",

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publisher = "Walter de Gruyter GmbH",

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T1 - Monotonicity formulae and curvature equations

AU - Urbas, John

PY - 2003

Y1 - 2003

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AB - We derive local integral estimates and monotonicity formulae for certain curvature quantities related to hypersurfaces of prescribed k-th mean curvature. We use these to improve interior curvature bounds established in previous work, and to derive a local Hölder gradient estimate for admissible solutions of the equation of prescribed scalar curvature.

UR - https://www.scopus.com/pages/publications/0037279236

U2 - 10.1515/crll.2003.031

DO - 10.1515/crll.2003.031

M3 - Article

SN - 0075-4102

SP - 199

EP - 218

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 557

ER -

Monotonicity formulae and curvature equations

Abstract

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