The Poisson equation on manifolds with positive essential spectrum
Differential Geometry
2019-09-06 v4 Analysis of PDEs
Abstract
We show existence of solutions to the Poisson equation on Riemannian manifolds with positive essential spectrum, assuming a sharp pointwise decay on the source function. In particular we can allow the Ricci curvature to be unbounded from below. In comparison with previous works, we can deal with a more general setting both on the spectrum and on the curvature bounds.
Keywords
Cite
@article{arxiv.1803.10167,
title = {The Poisson equation on manifolds with positive essential spectrum},
author = {Giovanni Catino and Dario Daniele Monticelli and Fabio Punzo},
journal= {arXiv preprint arXiv:1803.10167},
year = {2019}
}