Optimal bounds for ancient caloric functions
Optimal bounds for ancient caloric functions
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DOI：
10.1215/00127094-2021-0015
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发表时间：
2019-02
影响因子：
2.5
通讯作者：
T. Colding;W. Minicozzi
中科院分区：
文献类型：
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作者：
T. Colding;W. Minicozzi
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.
