Interior curvature bounds for a type of mixed Hessian quotient equations

Weimin Sheng; Shucan Xia; Weimin Sheng; Shucan Xia

doi:10.3934/mine.2023040

Mathematics in Engineering

2023, Volume 5, Issue 2: 1-27. doi: 10.3934/mine.2023040

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Interior curvature bounds for a type of mixed Hessian quotient equations

Weimin Sheng ^,,
Shucan Xia

School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

Received: 03 April 2022 Revised: 26 May 2022 Accepted: 26 May 2022 Published: 16 June 2022

We derive interior curvature bounds for admissible solutions of a class of mixed Hessian curvature equations subject to affine Dirichlet data. As an application, we study a Plateau type problem for locally convex Weingarten hypersurfaces.
- prescribed curvature problems,
- mixed Hessian quotient equations,
- curvature estimates
Citation: Weimin Sheng, Shucan Xia. Interior curvature bounds for a type of mixed Hessian quotient equations[J]. Mathematics in Engineering, 2023, 5(2): 1-27. doi: 10.3934/mine.2023040

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Abstract

We derive interior curvature bounds for admissible solutions of a class of mixed Hessian curvature equations subject to affine Dirichlet data. As an application, we study a Plateau type problem for locally convex Weingarten hypersurfaces.

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