Ratio limit theorem for parabolic horn-shaped domains

Collet, Pierre; Martinez, Servet; San Martin, Jaime

doi:10.1090/S0002-9947-06-03908-0

Ratio limit theorem for parabolic horn-shaped domains
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by Pierre Collet, Servet Martinez and Jaime San Martin PDF

Trans. Amer. Math. Soc. 358 (2006), 5059-5082 Request permission

Abstract:

We prove that for horn-shaped domains of parabolic type, the ratio of the heat kernel at different fixed points has a limit when the time tends to infinity. We also give an explicit formula for the limit in terms of the harmonic functions.

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