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1 December 2021 Optimal bounds for ancient caloric functions
Tobias Holck Colding, William P. Minicozzi II
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Duke Math. J. 170(18): 4171-4182 (1 December 2021). DOI: 10.1215/00127094-2021-0015

Abstract

For any manifold with polynomial volume growth, we show that 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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Tobias Holck Colding. William P. Minicozzi II. "Optimal bounds for ancient caloric functions." Duke Math. J. 170 (18) 4171 - 4182, 1 December 2021. https://doi.org/10.1215/00127094-2021-0015

Information

Received: 26 February 2019; Revised: 2 February 2021; Published: 1 December 2021
First available in Project Euclid: 18 November 2021

Digital Object Identifier: 10.1215/00127094-2021-0015

Subjects:
Primary: 53C21
Secondary: 53C44

Keywords: caloric , Geometric flows , Harmonic functions , polynomial growth

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 18 • 1 December 2021
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