A note on the scattering theory of Kato-Ricci manifolds
Spectral Theory
2024-11-06 v1 Differential Geometry
Abstract
In this note we prove a new criterion for the existence and completeness of the wave operators corresponding to the Laplace-Beltrami operators corresponding to two Riemannian metrics on a fixed noncompact manifold. Our result relies on recent estimates on the heat semigroup and its derivative, that are valid if the negative part of the Ricci curvature is in the Kato class - so called Kato-Ricci manifolds.
Keywords
Cite
@article{arxiv.2411.03204,
title = {A note on the scattering theory of Kato-Ricci manifolds},
author = {Batu Güneysu and Maxime Marot},
journal= {arXiv preprint arXiv:2411.03204},
year = {2024}
}