Heat Kernel Estimates Under the Ricci–Harmonic Map Flow

Mihai Băileşteanu, Hung Tran

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This paper considers the Ricci flow coupled with the harmonic map flow between two manifolds. We derive estimates for the fundamental solution of the corresponding conjugate heat equation and we prove an analogue of Perelman's differential Harnack inequality. As an application, we find a connection between the entropy functional and the best constant in the Sobolev embedding theorem in ℝn.

Original languageEnglish
Pages (from-to)1-27
Number of pages27
JournalProceedings of the Edinburgh Mathematical Society
StateAccepted/In press - Feb 22 2017


  • Ricci flow
  • Sobolev embedding
  • differential Harnack inequality
  • harmonic map
  • heat equation
  • heat kernel


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