Conformal deformation of metrics on subdomains of surfaces

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

Journal Title

The Journal of Geometric Analysis

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