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Is there a version of Varadhan's lemma for heat-kernels on Finsler manifolds? I expect this to exist but I cannot seem to find any papers on the topic. References would be greatly appreciated.

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    $\begingroup$ The problem is that the heat equation for a Finsler metric is nonlinear, so there is no heat kernel per se. $\endgroup$
    – Deane Yang
    Commented Mar 2, 2017 at 4:14
  • $\begingroup$ If I assume the finsler function is L^p norm on the tangent spaces.would that help? $\endgroup$
    – ABIM
    Commented Mar 2, 2017 at 4:40
  • $\begingroup$ Perhaps you should first make precise what you mean by a heat kernel. $\endgroup$
    – Deane Yang
    Commented Mar 2, 2017 at 14:17
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    $\begingroup$ You can find several papers if you google "heat flow Finsler". if you want to define the heat flow in terms of a "Finsler Laplacian", which in turn is defined using an energy functional analogous to the $L^2$ norma of the gradient, then everything is nonlinear. Even for the $L^p$ norm. You can do the calculations yourself. $\endgroup$
    – Deane Yang
    Commented Mar 3, 2017 at 1:05
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    $\begingroup$ You can also google "p-Laplacian heat flow" $\endgroup$
    – Deane Yang
    Commented Mar 3, 2017 at 1:08

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