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

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

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number108968
JournalJournal of Functional Analysis
Volume280
Issue number10
DOIs
Publication statusPublished - 2021 May 15

Keywords

  • Heat kernel
  • Laplacian
  • Metric measure spaces
  • Ricci curvature

ASJC Scopus subject areas

  • Analysis

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