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2 votes

Gaussian upper heat kernel bounds on closed Riemannian manifolds

This is related to Li-Yau gradient estimates. I think the usual set up is for a complete manifold with $\textrm{Ric}(M)>-k$. You probably need some Harnark type inequalities for parabolic equations. I …
Bombyx mori's user avatar
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7 votes
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How to interpret heat kernel at unit time on a Riemann surface?

Let $M$ be a compact Riemann Surface. Let $P$ be a fixed point on $M$ and let $\delta_{P}$ be the Dirac point distribution at $M$. Consider the fundamental solution of the heat equation $$ (\partial_{ …
Bombyx mori's user avatar
  • 6,249