Intrinsic flat convergence of covering spaces

DOI10.1007/S10711-016-0158-0zbMath1358.58015arXiv1409.7118OpenAlexW2275004233MaRDI QIDQ329337

Christina Sormani, Zahra Sinaei

Publication date: 21 October 2016

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.7118

zbMATH Keywords

covering spacegeodesic metric spacecovering spectrumintrinsic flat convergence

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Isospectrality (58J53)

Cites Work

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• Smooth convergence away from singular sets
• Isospectral surfaces with distinct covering spectra via Cayley graphs
• Sunada's method and the covering spectrum
• The intrinsic flat distance between Riemannian manifolds and other integral current spaces
• Compactness for manifolds and integral currents with bounded diameter and volume
• The pointed flat compactness theorem, for locally integral currents
• Manifolds near the boundary of existence
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Intrinsic flat Arzela-Ascoli theorems
• Discrete homotopies and the fundamental group
• The revised and uniform fundamental groups and universal covers of geodesic spaces
• Describing the universal cover of a compact limit
• Noncompact manifolds with nonnegative Ricci curvature
• The covering spectrum of a compact length space
• Hausdorff convergence and universal covers
• Currents in metric spaces

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