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Results tagged with laplacian
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user 13093
The Laplacian matrix is the representation of a graph in matrix form.
8
votes
First eigenvalue of the Laplacian on a regular polygon
For $N \geq 5$ it is still not known if the $N$-gon which minimizes the first eigenvalue under area constraint (which exists), is the regular one. I have done some numerical computations which suggest …
- 2,222
2
votes
First eigenvalue of the Laplacian on a regular polygon
Some recent activity on the problem:
Results regarding the Hessian matrix with respect to vertex coordinates, numerical local minimality estimates and analytical bounds on the diameter of the optimal …
- 2,222
3
votes
1
answer
164
views
Analytical value for the first eigenvalue of a certain spherical triangle
I am testing some numerical algorithms for computing the Laplace-Beltrami eigenvalues on the sphere. One thing that came up was computing the first eigenvalue of the "equilateral" spherical triangle w …
- 44.4k
1
vote
Spectrum of Dirichlet Problem for Laplacian on a Parallelogram
This may not be what you wish for, but here is a list of the first $10$ eigenvalues calculated numerically for the rhombus with sidelength $1$:
$$\begin{array}{c}24.8982\\
52.6379\\
71.7085\\
…
- 2,222