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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

1 vote
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Exponential decay of resolvent kernel

The local statement is correct for any positive self-adjoint extension of the Laplace operator on a Riemannian manifold (not necessarily complete). It is an old result by Hoermander. See the proof of …
Alexander Strohmaier's user avatar
5 votes

Fredholm theory of non elliptic operators

I think I am in a good position to answer this. The Fredholm property of elliptic operators as maps between Sobolev spaces on compact manifolds rests on elliptic regularity properties. If an operators …