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arXiv · 2512.13952

Ancient Solutions to the Biharmonic Heat Equation

Alexander D. McWeeney
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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.

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Alexander D. McWeeney. 2025-12-15. Ancient Solutions to the Biharmonic Heat Equation. https://arxiv.org/abs/2512.13952

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