Large time behavior of the heat kernel: The parabolic \(\lambda\)-potential alternative (Q1190207)

This article is devoted to the proof of the parabolic \(\lambda\)-potential alternative. The authors study large time behavior of the minimal positive heat kernel \(p(x,y,t)\), where \((x,y,t)\) is an element of \(M\times M\times (0,\infty)\), \(M\) is a noncompact Riemannian manifold with Laplace-Beltrami operator \(\Delta\) acting on functions on \(M\) and \(\lambda\) is the bottom of \(\text{spec}(-\Delta)\).