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

3 Scopus citations


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
Number of pages20
StatePublished - 2020

Publication series

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

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


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


Dive into the research topics of 'Some Remarks on the Geometry of a Class of Locally Conformally Flat Metrics'. Together they form a unique fingerprint.

Cite this