Counterexamples to C2 boundary estimates for a fully nonlinear Yamabe problem on manifolds with boundary

Yan Yan Li, Luc Nguyen

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

On closed manifolds, gradient and Hessian a priori estimates for fully nonlinear Yamabe problems are known to hold. On manifolds with boundary, gradient estimates are known to hold, while Hessian estimates hold if the prescribed mean curvature is positive. Examples are given here which show that Hessian estimates can fail when the mean curvature is negative.

Original languageEnglish (US)
Pages (from-to)783-797
Number of pages15
JournalAdvanced Nonlinear Studies
Volume12
Issue number4
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematics(all)

Keywords

  • Counterexample
  • Elliptic
  • Fully nonlinear
  • Yamabe

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