Strictly locally convex hypersurfaces with prescribed curvature and boundary in space forms

Zhenan Sui

doi:10.1080/03605302.2019.1670675

Strictly locally convex hypersurfaces with prescribed curvature and boundary in space forms

Zhenan Sui^*

^*Corresponding author for this work

School of Mathematics

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

4 Scopus citations

Abstract

This article is devoted to C² a priori estimates for strictly locally convex radial graphs with prescribed Weingarten curvature and boundary in space forms. By constructing two-step continuity process and applying degree theory arguments, existence results in space forms are established for prescribed Gauss curvature equation under the assumption of a strictly locally convex subsolution.

Original language	English
Pages (from-to)	253-283
Number of pages	31
Journal	Communications in Partial Differential Equations
Volume	45
Issue number	3
DOIs	https://doi.org/10.1080/03605302.2019.1670675
State	Published - 3 Mar 2020

Keywords

Hypersurfaces of prescribed curvature
boundary
space forms

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10.1080/03605302.2019.1670675

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title = "Strictly locally convex hypersurfaces with prescribed curvature and boundary in space forms",

abstract = "This article is devoted to C2 a priori estimates for strictly locally convex radial graphs with prescribed Weingarten curvature and boundary in space forms. By constructing two-step continuity process and applying degree theory arguments, existence results in space forms are established for prescribed Gauss curvature equation under the assumption of a strictly locally convex subsolution.",

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AB - This article is devoted to C2 a priori estimates for strictly locally convex radial graphs with prescribed Weingarten curvature and boundary in space forms. By constructing two-step continuity process and applying degree theory arguments, existence results in space forms are established for prescribed Gauss curvature equation under the assumption of a strictly locally convex subsolution.

KW - Hypersurfaces of prescribed curvature

KW - boundary

KW - space forms

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DO - 10.1080/03605302.2019.1670675

M3 - 文章

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

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Strictly locally convex hypersurfaces with prescribed curvature and boundary in space forms

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Keywords

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