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Results tagged with laplacian
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user 15743
The Laplacian matrix is the representation of a graph in matrix form.
7
votes
1
answer
1k
views
Multiplicity of eigenvalues of the Laplacian on quaternionic projective space
By looking at eigenfunctions of the Laplacian on $S^n$,$S^{2n+1}$ and $S^{4n+3}$ (note they are the unit spheres of $\mathbb R^{n+1}$, $\mathbb C^{n+1}$ and $\mathbb H^{n+1}$) that are respectively invariant … QUESTION: Compute the multiplicity of the $k$-th eigenvalue $4k(k+2n+1)$ of the Laplacian on $\mathbb H P^n$. …
- 5,891
13
votes
1
answer
2k
views
First eigenvalue of the Laplacian on Berger spheres
In this context, the Laplacian $\Delta_t$ of the canonical variation can be related to the original Laplacian $\Delta_1$ in terms of the vertical Laplacian $\Delta_v$, by the formula $$\Delta_t=\Delta_ … \in Spec(\Delta_F)$ is an eigenvalue of the Laplacian of the fiber. …
- 5,891
22
votes
1
answer
960
views
Avoiding integers in the spectrum of the Laplacian of a Riemann surface
For a given metric $g$, denote by $Spec(\Delta_g)=\{0=\lambda_0<\lambda_1\leq\lambda_2\leq\dots\}$ the spectrum of the Hodge-Laplacian of $g$, acting on $C^\infty(\Sigma)$. …
- 5,891