Heat Content in Non-compact Riemannian Manifolds

M. van den Berg*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
233 Downloads (Pure)


Let Ω be an open set in a complete, smooth, non-compact, m-dimensional Riemannian manifold M without boundary, where M satisfies a two-sided Li-Yau gaussian heat kernel bound. It is shown that if Ω has infinite measure, and if Ω has finite heat content HΩ(T) for some TCloseSPigtSPi 0 , then HΩ(t) OpenSPiltSPi ∞ for all tCloseSPigtSPi 0. Comparable two-sided bounds for HΩ(t) are obtained for such Ω.

Original languageEnglish
Article number8
Number of pages15
JournalIntegral Equations and Operator Theory
Issue number1
Publication statusPublished - 28 Feb 2018


  • Heat content
  • Poincaré inequality
  • Riemannian manifold
  • Volume doubling

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