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asked What is the hyperbolic plane equivalent to translation in euclidean space
Aug
18
comment Dirichlet Eigenvalues of Laplace-Beltrami operator in Hyperbolic space
Thank you, but I couldn't find an example in this book for the above Laplace-Beltrami Operator. Do you know on what page Chavel gives an example?
Aug
18
revised Dirichlet Eigenvalues of Laplace-Beltrami operator in Hyperbolic space
added 162 characters in body
Aug
18
asked Dirichlet Eigenvalues of Laplace-Beltrami operator in Hyperbolic space
Aug
10
accepted Integral over compact boundary is finite in the context of potential function
Aug
10
comment Integral over compact boundary is finite in the context of potential function
Thank you very much! This was a nice idea, which I have to keep in mind. Best Regards.:-)
Aug
9
comment Integral over compact boundary is finite in the context of potential function
I know the definition, but I have not much experience in calculation of integrals over surfaces. Suppose we want to calculate the integral over some domain $\partial\Omega\cap B_{\epsilon}(x_0)$ for some small $\epsilon >0$. Then one would take some coordinate chart $\varphi: U\rightarrow \partial \Omega\cap B_{\epsilon}(x_0)$ and the integral one has to solve should be: $\int_{U}\Vert\varphi(x)-x_0 \Vert^{-n+\frac{3}{2}}dx$. Unfortunately I don't see how this integral is finite....
Aug
9
asked Integral over compact boundary is finite in the context of potential function
Aug
5
accepted A proposition about two sequences
Aug
5
accepted why is the spectrum of the schrödinger operator discrete?
Aug
5
accepted inner product on matrices with quaternionic entries
Aug
5
accepted Why is the laplacian positive-definite
Aug
5
accepted integration over a ball
Aug
5
accepted Estimate for boundary points and exterior normal vector of bounded domain of class $C^2$
Jul
29
comment Estimate for boundary points and exterior normal vector of bounded domain of class $C^2$
Yes. But $x_0$ is also some arbitrary fixed point on the boundary
Jul
29
asked Estimate for boundary points and exterior normal vector of bounded domain of class $C^2$
Jul
2
awarded  Curious
Apr
29
comment Integrate $\int_{-\infty}^{\infty}\exp\left(-\frac{\pi^2t(2x+1)^2}{2c^2}\right)\cos\left(\frac{(2x+1)\pi y}{c}\right)\exp(-2\pi i kx)dx$
Thank you so much!!
Apr
29
accepted Integrate $\int_{-\infty}^{\infty}\exp\left(-\frac{\pi^2t(2x+1)^2}{2c^2}\right)\cos\left(\frac{(2x+1)\pi y}{c}\right)\exp(-2\pi i kx)dx$
Apr
29
awarded  Custodian