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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?