Ancient Solutions to the Biharmonic Heat Equation
arXiv:2512.13952
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.
arXiv comment12 pages