Nodal domains and growth of harmonic functions on noncompact manifolds

Harold Donnelly, Charles Fefferman

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

Harmonic functions are studied on complete Riemannian manifolds. A decay estimate is given for bounded harmonic functions of variable sign. For unbounded harmonic functions of variable sign, relations are derived between growth properties and nodal domains. On Riemannian manifolds of nonnegative Ricci curvature, it has been conjectured that harmonic functions, having at most a given order of polynomial growth, must form a finite dimensional vector space. This conjecture is established in certain special cases.

Original languageEnglish (US)
Pages (from-to)79-93
Number of pages15
JournalThe Journal of Geometric Analysis
Volume2
Issue number1
DOIs
StatePublished - Jan 1 1992

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Harmonic functions
  • Math Subject Classification: 58G99
  • Riemannian manifolds
  • nodal domains
  • nonnegative Ricci curvature
  • polynomial growth

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