Intrinsic Ultracontractivity for Domains in Negatively Curved Manifolds

Aikawa, Hiroaki; van den Berg, Michiel; Masamune, Jun

Computational Methods and Function Theory, 2021, 21, 797-824

Permalink : https://hdl.handle.net/2115/82920

このアイテムのアクセス数:397件（2026-08-26 07:15 集計）

ファイル	フォーマット	サイズ	閲覧回数	説明
https://doi.org/10.1007/s40315-021-00402-8			9

アクセス権	open access
URI	https://hdl.handle.net/2115/82920
タイトル	Intrinsic Ultracontractivity for Domains in Negatively Curved Manifolds
著者	Aikawa, Hiroaki ; van den Berg, Michiel ; Masamune, Jun
著者名 Aikawa, Hiroaki
著者名 van den Berg, Michiel
著者名 Masamune, Jun
言語	英語
キーワード	Intrinsic ultracontractivity
	Ricci curvature
	First eigenvalue
	Heat kernel
	Torsion function
	Capacitary width
発行日	2021-10-12
出版者	Springer
収録物名	Computational Methods and Function Theory
巻(号)	21
ページ	797-824
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 forwhich 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 L-2(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 Poincare inequality and the Li-Yau Gaussian estimate for the Dirichlet heat kernel at finite scale.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
PISSN	1617-9447
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.1007/s40315-021-00402-8