Embedding of RCD(K,N) spaces in L2 via eigenfunctions

Luigi Ambrosio, Shouhei Honda, Jacobus W. Portegies, David Tewodrose

研究成果: Article査読

抄録

In this paper we study the family of embeddings Φt of a compact RCD(K,N) space (X,d,m) into L2(X,m) via eigenmaps. Extending part of the classical results [10,11] known for closed Riemannian manifolds, we prove convergence as t↓0 of the rescaled pull-back metrics ΦtgL2 in L2(X,m) induced by Φt. Moreover we discuss the behavior of ΦtgL2 with respect to measured Gromov-Hausdorff convergence and t. Applications include the quantitative Lp-convergence in the noncollapsed setting for all p<∞, a result new even for closed Riemannian manifolds and Alexandrov spaces.

本文言語English
論文番号108968
ジャーナルJournal of Functional Analysis
280
10
DOI
出版ステータスPublished - 2021 5 15

ASJC Scopus subject areas

  • 分析

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