Ancient Solutions to the Biharmonic Heat Equation
Differential Geometry
2026-03-02 v2 Analysis of PDEs
Abstract
We show that the space of polynomially bounded ancient solutions to the biharmonic heat equation on a complete manifold with polynomial volume growth is bounded by the dimensions of spaces of polynomially bounded biharmonic functions. This generalizes the work of Colding and Minicozzi in [6] for ancient caloric functions.
Cite
@article{arxiv.2512.13952,
title = {Ancient Solutions to the Biharmonic Heat Equation},
author = {Alexander D. McWeeney},
journal= {arXiv preprint arXiv:2512.13952},
year = {2026}
}
Comments
12 pages