Classic definition of heat kernel

[pabryan]

Fix rem 3.3. Find out what is meant by a definition in the classical setting for noncompact manifolds when they construct this heat kernel via a limit, and show that either our notion of a function is sufficiently weak to capture the classic shit or it is necessary for us to formulate the problem in this way because we don't have the classical methods at hand

[lashputin]

SO, they look at domains \Omega \subset M, and then they look at the heat kernel associated with the Dirichlet problem in \Omega, and then they show that you can extract a limit from these heat kernels. They call this the "minimal" heat kernel. We should point out that we don't consider this because this minimal heat kernel, in general, doesn't satisfy good properties.