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Results tagged with laplacian
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user 1441
The Laplacian matrix is the representation of a graph in matrix form.
4
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Accepted
Lower bound on the first eigenvalue of the Laplacian of a Riemann surface with constant nega...
I guess you mean constant curvature $=-1$; otherwise you get an example by rescaling.
On a sphere with two handles there are metrics with curvature $\equiv-1$ which look roughly as a long neck attach …
- 45k
14
votes
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Growth of Laplacian eigenvalues on a compact domain?
Weyl's formula:
$$N(R)=\frac{1}{(4{\cdot}\pi)^{d/2}{\cdot}\Gamma\left(\frac d2+1\right)}{\cdot}V{\cdot}R^{d/2}+o(R^{d/2}).$$
where $d$ --- dimension, $V$ --- volume, $N(R)$ --- number of eigenvalues …
- 45k