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Conformal deformation of metrics on subdomains of surfaces

The Journal of Geometric Analysis volume 5, pages 395–410 (1995)Cite this article

Abstract

We consider prescribing Gaussian curvature on subdomains of a surface. We employ thedistribution 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.

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Authors and Affiliations

  1. Department of Mathematics, Southwest Missouri State University, 65804, Springfield, MO

    Kanghui Guo & Shouchuan Hu

Authors
  1. Kanghui Guo
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  2. Shouchuan Hu
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Additional information

Communicated by Jerry L. Kazdan

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Guo, K., Hu, S. Conformal deformation of metrics on subdomains of surfaces. J Geom Anal 5, 395–410 (1995). https://doi.org/10.1007/BF02921803

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  • DOI: https://doi.org/10.1007/BF02921803

Math Subject Classification

  • 35J20
  • 35J60
  • 53C99

Key Words and Phrases

  • conformal mappings
  • Neumann problem
  • variational methods
  • isoperimetric inequalitie