Intrinsic Ultracontractivity for Domains in Negatively Curved Manifolds

Hiroaki Aikawa, Michiel van den Berg, Jun Masamune

研究成果: Article査読

抄録

Let M be a complete, non-compact, connected Riemannian manifold with Ricci curvature bounded from below by a negative constant. A sufficient condition is obtained for open and connected sets D in M for which the corresponding Dirichlet heat semigroup is intrinsically ultracontractive. That condition is formulated in terms of capacitary width. It is shown that both the reciprocal of the bottom of the spectrum of the Dirichlet Laplacian acting in L2(D) , and the supremum of the torsion function for D are comparable with the square of the capacitary width for D if the latter is sufficiently small. The technical key ingredients are the volume doubling property, the Poincaré inequality and the Li-Yau Gaussian estimate for the Dirichlet heat kernel at finite scale.

本文言語English
ページ(範囲)797-824
ページ数28
ジャーナルComputational Methods and Function Theory
21
4
DOI
出版ステータスPublished - 2021 12月
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 計算理論と計算数学
  • 応用数学

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