The Pogorelov Estimates for Degenerate Curvature Equations
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.
Authors
- Heming Jiao (ORCID: https://orcid.org/0000-0002-6595-8303)
- Yang Jiao (ORCID: https://orcid.org/0000-0001-6501-8787)
Institutions
- Harbin Institute of Technology (CN)
- Heilongjiang Institute of Technology (CN)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2024-08-12
- DOI
- https://doi.org/10.1093/imrn/rnae161
- Citations
- 2
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 1.95
Funders
- National Natural Science Foundation of China
- Natural Science Foundation of Heilongjiang Province
- Fundamental Research Funds for the Central Universities