Dimensional bounds for ancient caloric functions on graphs
Differential Geometry
2019-03-12 v2 Combinatorics
Metric Geometry
Abstract
We study ancient solutions of polynomial growth to heat equations on graphs, and extend Colding and Minicozzi's theorem [CM19] on manifolds to graphs: For a graph of polynomial volume growth, the dimension of the space of ancient solutions of polynomial growth is bounded by the product of the growth degree and the dimension of harmonic functions with the same growth.
Cite
@article{arxiv.1903.02411,
title = {Dimensional bounds for ancient caloric functions on graphs},
author = {Bobo Hua},
journal= {arXiv preprint arXiv:1903.02411},
year = {2019}
}
Comments
12 pages