The Journal of Geometric Analysis

, Volume 2, Issue 1, pp 79–93 | Cite as

Nodal domains and growth of harmonic functions on noncompact manifolds

  • Harold Donnelly
  • Charles Fefferman


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.

Math Subject Classification


Key Words and Phrases

Harmonic functions nodal domains nonnegative Ricci curvature polynomial growth Riemannian manifolds 


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Copyright information

© Mathematica Josephina, Inc. 1992

Authors and Affiliations

  • Harold Donnelly
    • 1
    • 2
  • Charles Fefferman
    • 1
    • 2
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA

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