Conformal deformation of metrics on subdomains of surfaces

Authors

Kanghui Guo, Missouri State UniversityFollow
Shouchuan Hu, Missouri State UniversityFollow

Abstract

We consider prescribing Gaussian curvature on subdomains of a surface. We employ the distribution of mass principle (Theorem 3.3) to smooth subdomains of a Riemannian manifold to obtain that for critical and supercritical cases, a function can be the Gaussian curvature of some pointwise conformal metric, provided it satisfies certain conditions.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1007/BF02921803

Keywords

conformal mappings, isoperimetric inequalitie, Math Subject Classification: 35J20, 35J60, 53C99, Neumann problem, variational methods

Publication Date

9-1-1995

Recommended Citation

Guo, Kanghui, and Shouchuan Hu. "Conformal deformation of metrics on subdomains of surfaces." The Journal of Geometric Analysis 5, no. 3 (1995): 395-410.

Journal Title

The Journal of Geometric Analysis