Well I have little experience with pde's and analysis, I mostly study topic related to geometric topology and I would like to see if someone can please explain to me why is it important to find bounds on eigenvalues of elliptic operators on functions on riemannian manifolds. To be a little more specific, I think that these are used to get some information about the underlying manifold and I would like to know what kind of geometric (or even topologic, if any) properties can one obtain by finding bounds on the first eigenvalues of some operator. I mean if this is the reason why one would try to find these kind of bounds, if not well maybe you can show me some light as to how is these useful. Thanks.
2026-05-05 20:20:17.1778012417
bounds on eigenvalues of elliptic operators on functions on riemannian manifolds
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