English

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 L1L^1 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}
}