Polynomial growth harmonic functions on complete Riemannian manifolds

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Abstract

In this paper, we give a sharp estimate on the dimension of the space of polynomial growth harmonic functions with fixed degree on a complete Riemannian manifold, under various assumptions.

Original languageEnglish
Pages (from-to)315-332
Number of pages18
JournalRevista Matematica Iberoamericana
Volume20
Issue number2
DOIs
StatePublished - 2004

Keywords

  • Mean value property
  • Poincaré inequality
  • Polynomial growth harmonic function
  • Volume doubling condition

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