The global behavior of heat kernels in exterior domains
It is established the global boundary behavior of Dirichlet heat kernels on some unbounded \(C^{1,1}\) domains \(D\subset M\) where \(M\) is a complete noncompact manifold with nonnegative Ricci curvature. These, combined with the interior estimate in the recent paper of \textit{A. Grigoryan} and \textit{L. Saloff-Coste} [Commun. Pure Appl. Math. 55, 93-133 (2002; Zbl 1037.58018)], provide a complete and qualitatively sharp description of heat kernels \(G\) of Dirichlet Laplacian.
scientific article; zbMATH DE number 1915625