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arXiv · 1902.01736

Optimal bounds for ancient caloric functions

Tobias Holck Colding·William P. Minicozzi II
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Abstract

For any manifold with polynomial volume growth, we show: The dimension of the space of ancient caloric functions with polynomial growth is bounded by the degree of growth times the dimension of harmonic functions with the same growth. As a consequence, we get a sharp bound for the dimension of ancient caloric functions on any space where Yau's 1974 conjecture about polynomial growth harmonic functions holds.

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BibTeXRIS

Tobias Holck Colding, William P. Minicozzi II. 2019-02-05. Optimal bounds for ancient caloric functions. https://arxiv.org/abs/1902.01736

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