Diffusion determines the manifold
Analysis of PDEs
2008-06-04 v1
Abstract
We prove under a weak smoothness condition that two Riemannian manifold are isomorphic if and only there exists an order isomorphism which intertwines with the Dirichlet type heat semigroups on the manifolds.
Cite
@article{arxiv.0806.0437,
title = {Diffusion determines the manifold},
author = {Wolfgang Arendt and Markus Biegert and A. F. M. ter Elst},
journal= {arXiv preprint arXiv:0806.0437},
year = {2008}
}