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 Dec 7 awarded Popular Question Oct 15 accepted Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$? Oct 15 comment Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$? I think there is a problem with your approach, since the integral $\int_d^{d+1}\frac{1}{(\cosh(s)-\cosh(d))^{3/2}} ds$ do not converge, so that it is not justified to change integral and derivative. Oct 14 comment Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$? Yes, your idea is nice! But it seems not clear to me how to compute the derivative $\partial_d k(r,d)$ or to estimate it. Oct 14 revised Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$? added 129 characters in body Oct 14 revised Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$? added 71 characters in body; edited title Oct 13 asked Is the heat kernel for the hyperbolic plane uniformly continuous in $t\in(0,\infty)$? Feb 17 accepted Fundamental solution to the heat equation with zero boundary values Feb 17 asked Fundamental solution to the heat equation with zero boundary values Jan 27 accepted holomorphic continuation Jan 26 asked holomorphic continuation Dec 1 accepted Formula for the Perimeter of a spherical triangle? Dec 1 comment Formula for the Perimeter of a spherical triangle? Thanks for your help! This is a nice formula. In my understanding this formula doesn't work for triangles with any of its lengths $\ell_i>\pi$. Do you agree or am I missing something? Dec 1 asked Formula for the Perimeter of a spherical triangle? Sep 7 comment Boundary regularity of Dirichlet Eigenfunction on bounded domains Thank you very much! @Christian: Why should there be a problem? Do you have an exceptional situation in mind? Sep 6 asked Boundary regularity of Dirichlet Eigenfunction on bounded domains Aug 7 comment construction of heat kernels for non-compact manifolds with boundary Did you find an answer to your question in meanwhile? I'm wondering, if one can construct the dirichlet heat kernel for unbounded domains with boundary this way (e.g. unbounded domains in euclidean space). Aug 4 comment Existence of the Dirichlet heat kernel for arbitrary open subsets? @Chrisitan: Thank you! What do you mean by $e^{t\Delta}$? In my experience this symbol occurs in two situations. First in the context of 'continuous functional calculus'. And second in the theory of 'strongly continuous semigroups'. Maybe all of them correspond to the same operator, but I'm not sure. I would be very glad, if you can explain it to me? Aug 3 accepted How to evaluate the wiener measure of sets? Aug 3 asked Existence of the Dirichlet heat kernel for arbitrary open subsets?