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<p>Under a condition that breaks the volume doubling barrier, we obtain a time polynomial structure result on the space of ancient caloric functions with polynomial growth on manifolds. As a byproduct, it is shown that the finiteness result for the space of harmonic functions with polynomial growth on manifolds in [<CitationRef CitationID="CR9">9</CitationRef>] and [<CitationRef CitationID="CR23">23</CitationRef>] are essentially sharp, except for the multi-end cases, addressing an issue raised in [<CitationRef CitationID="CR11">11</CitationRef>] and removing all <i>local</i> topological or geometric conditions on the manifold with respect to a reference point.</p>

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Space of Ancient Caloric Functions on Some Manifolds Beyond Volume Doubling

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Fanghua Lin,
  • Hongbing Qiu,
  • Jun Sun,
  • Qi S. Zhang

摘要

Under a condition that breaks the volume doubling barrier, we obtain a time polynomial structure result on the space of ancient caloric functions with polynomial growth on manifolds. As a byproduct, it is shown that the finiteness result for the space of harmonic functions with polynomial growth on manifolds in [9] and [23] are essentially sharp, except for the multi-end cases, addressing an issue raised in [11] and removing all local topological or geometric conditions on the manifold with respect to a reference point.