Work

The Pogorelov Estimates for Degenerate Curvature Equations

Year: 2024

Type: article

Abstract: We establish the Pogorelov-type estimates for degenerate prescribed $k$-curvature equations as well as $k$-Hessian 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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnae161

Authors: Heming Jiao, Yang Jiao

Institution: Harbin Institute of Technology

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Heilongjiang Province, Fundamental Research Funds for the Central Universities

Awards: G133574114, G2042295377, G7899643992