Poisson equation on complete manifolds

Ovidiu Munteanu, Chiung Jue Anna Sung, Jiaping Wang

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We develop heat kernel and Green's function estimates for manifolds with positive bottom spectrum. The results are then used to establish existence and sharp estimates of the solution to the Poisson equation on such manifolds with Ricci curvature bounded below. As an application, we show that the curvature of a steady gradient Ricci soliton must decay exponentially if it decays faster than linear and the potential function is bounded above.

Original languageEnglish (US)
Pages (from-to)81-145
Number of pages65
JournalAdvances in Mathematics
Volume348
DOIs
StatePublished - May 25 2019

Keywords

  • Bottom spectrum
  • Green's function
  • Poisson equation
  • Steady Ricci solitons

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