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Results tagged with laplacian
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user 4572
The Laplacian matrix is the representation of a graph in matrix form.
10
votes
First nonzero eigenvalue of the Laplacian on the submanifold
In the general case (especially for high codimension) there will not be such a relation: Every compact Riemannian manifold can be isometrically embedded into the Euclidean space $R^N$. As the image of …
- 6,825
5
votes
Accepted
Realization of symbol of Laplace operator via certain integral
No: the operator must be of even order, and therefore the symbol of the adjoint operator $D^*$ is the same as the symbol of $D$. Hence we can assume without loss of generality that $D$ is symmetric. B …
- 6,825
10
votes
Accepted
Adjoint of a Connection Using the Hodge Map?
Yes, even in a more general situation: Let $E\to M$ be a vector bundle with metric and metric connection $\nabla.$ Then there exists $d^\nabla\colon\Omega^k(M,E)\to\Omega^{k+1}(M,E)$ satisfying $d^\na …
- 6,825