On the biharmonic heat equation on complete Riemannian manifolds
Differential Geometry
2022-03-29 v1
Abstract
We study entire solutions of the biharmonic heat equation on complete Riemannian manifolds without boundary. We provide exponential decay estimates for the biharmonic heat kernel under assumptions on the lower bound of Ricci curvature and noncollapsing of unit balls. And we prove a uniqueness criteria for the Cauchy problem. As corollaries we prove the conservation law for the biharmonic heat kernel and a uniform L-infinite estimate for entire solutions starting with bounded initial data.
Keywords
Cite
@article{arxiv.2203.14734,
title = {On the biharmonic heat equation on complete Riemannian manifolds},
author = {Fei He},
journal= {arXiv preprint arXiv:2203.14734},
year = {2022}
}
Comments
To appear on the Journal of Geometric Analysis S.I.: Analysis and Geometry on Complete manifolds