Some Remarks on the Geometry of a Class of Locally Conformally Flat Metrics

Sun Yung A. Chang, Zheng Chao Han, Paul Yang

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We prove that conformal metrics on domains of the round sphere, with non-negative constant Q-curvature, and non-negative scalar curvature, has positive mean curvature on the boundary of embedded balls (in the round metric). As a result, such metrics have certain reflection symmetries if the complement of the domain is contained in a lower-dimensional round sphere. We also prove that the development map of a locally conformally flat metric with non-positive Schouten tensor is an embedding.

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherBirkhauser
Pages37-56
Number of pages20
DOIs
StatePublished - 2020

Publication series

NameProgress in Mathematics
Volume333
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Keywords

  • 53C21
  • Conformal metrics
  • moving planes
  • moving spheres
  • Primary 58J06
  • Q-curvature
  • Secondary 35B06
  • σk-curvature

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  • Cite this

    Chang, S. Y. A., Han, Z. C., & Yang, P. (2020). Some Remarks on the Geometry of a Class of Locally Conformally Flat Metrics. In Progress in Mathematics (pp. 37-56). (Progress in Mathematics; Vol. 333). Birkhauser. https://doi.org/10.1007/978-3-030-34953-0_3