A note on renormalized volume functionals

Sun Yung Alice Chang, Hao Fang, C. Robin Graham

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

New properties are derived of renormalized volume functionals, which arise as coefficients in the asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) manifold. A formula is given for the renormalized volume of an even-dimensional AHE manifold in terms of an arbitrary totally geodesic compactification. The second variation of renormalized volume functionals under conformal change is identified, and is used to show that Einstein metrics of nonzero scalar curvature are local extrema.

Original languageEnglish (US)
Pages (from-to)246-258
Number of pages13
JournalDifferential Geometry and its Application
Volume33
DOIs
StatePublished - Mar 1 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology
  • Computational Theory and Mathematics

Keywords

  • Asymptotically hyperbolic Einstein metric
  • Renormalized volume functionals

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