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<p>In this paper, we prove the dimension of the space of weighted caloric functions with polynomial growth is bounded by the degree of growth times the dimension of weighted harmonic functions with the same growth on any weighted Riemannian manifold with polynomial volume growth. This generalizes the results of Colding-Minicozzi[<CitationRef CitationID="CR5">5</CitationRef>].</p>

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Caloric functions on weighted Riemannian manifolds

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • Zhuo Chen,
  • Wei Zhang

摘要

In this paper, we prove the dimension of the space of weighted caloric functions with polynomial growth is bounded by the degree of growth times the dimension of weighted harmonic functions with the same growth on any weighted Riemannian manifold with polynomial volume growth. This generalizes the results of Colding-Minicozzi[5].