The Pogorelov Estimates for Degenerate Curvature Equations

Heming Jiao; Yang Jiao

doi:10.1093/imrn/rnae161

The Pogorelov Estimates for Degenerate Curvature Equations

Heming Jiao^*
, Yang Jiao

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

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

2 Scopus citations

Abstract

We establish the Pogorelov-type estimates for degenerate prescribed k-curvature equations as well as kHessian equations. Furthermore, we investigate the interior C^1,1 regularity of the solutions for Dirichlet problems. These techniques also enable us to improve the existence theorem for an asymptotic Plateau-type problem in hyperbolic space.

Original language	English
Pages (from-to)	12504-12529
Number of pages	26
Journal	International Mathematics Research Notices
Volume	2024
Issue number	18
DOIs	https://doi.org/10.1093/imrn/rnae161
State	Published - 1 Sep 2024
Externally published	Yes

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title = "The Pogorelov Estimates for Degenerate Curvature Equations",

abstract = "We establish the Pogorelov-type estimates for degenerate prescribed k-curvature equations as well as kHessian equations. Furthermore, we investigate the interior C1,1 regularity of the solutions for Dirichlet problems. These techniques also enable us to improve the existence theorem for an asymptotic Plateau-type problem in hyperbolic space.",

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AB - We establish the Pogorelov-type estimates for degenerate prescribed k-curvature equations as well as kHessian equations. Furthermore, we investigate the interior C1,1 regularity of the solutions for Dirichlet problems. These techniques also enable us to improve the existence theorem for an asymptotic Plateau-type problem in hyperbolic space.

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M3 - 文章

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JO - International Mathematics Research Notices

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The Pogorelov Estimates for Degenerate Curvature Equations

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