Large time behavior of the heat kernel

Yehuda Pinchover

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Large time behavior of the heat kernel

Yehuda Pinchover

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Abstract

In this paper we study the large time behavior of the (minimal) heat kernel $k_P^M(x,y,t)$ of a general time independent parabolic operator $L=u_t+P(x, \partial_x)$ which is defined on a noncompact manifold $M$. More precisely, we prove that $$\lim_{t\to\infty} e^{λ_0 t}k_P^{M}(x,y,t)$$ always exists. Here $λ_0$ is the generalized principal eigenvalue of the operator $P$ in $M$.

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Yehuda Pinchover. 2002-06-26. Large time behavior of the heat kernel. https://arxiv.org/abs/math/0206281

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