I've seen in an article, but they don't explain what is that exactly. In spectral geometry, what is a direct and inverse problem?


1 Answer 1


This is answered by the Wikipedia page for spectral geometry. I'll quote the bare minimum here; more detail is given at the linked page.

Inverse problems seek to identify features of the geometry from information about the eigenvalues of the Laplacian.


Direct problems attempt to infer the behaviour of the eigenvalues of a Riemannian manifold from knowledge of the geometry.


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