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differential harnack inequality

Proceedings of the Edinburgh Mathematical Society (1)

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1 results

Heat Kernel Estimates Under the Ricci–Harmonic Map Flow
Part of
- Global differential geometry
- Parabolic equations and systems
Mihai Băileşteanu, Hung Tran
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 60 / Issue 4 / November 2017

Published online by Cambridge University Press:

22 February 2017, pp. 831-857
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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 .