Ratio limit theorem for parabolic horn-shaped domains
Pierre Collet, Servet Martı́nez, Jaime San Martı́n · Transactions of the American Mathematical Society · 2006
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.