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

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

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 Φt⁎gL2 in L2(X,m) induced by Φt. Mo...

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Veröffentlicht in:Journal of functional analysis 2021-05, Vol.280 (10), p.108968, Article 108968
Hauptverfasser: Ambrosio, Luigi, Honda, Shouhei, Portegies, Jacobus W., Tewodrose, David
Format: Artikel
Sprache:eng
Schlagworte:
Heat kernel
Laplacian
Metric measure spaces
Ricci curvature
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Zusammenfassung: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 Φt⁎gL2 in L2(X,m) induced by Φt. Moreover we discuss the behavior of Φt⁎gL2 with respect to measured Gromov-Hausdorff convergence and t. Applications include the quantitative Lp-convergence in the noncollapsed setting for all p
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2021.108968