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May 2004 The covering spectrum of a compact length space
Christina Sormani, Guofang Wei
J. Differential Geom. 67(1): 35-77 (May 2004). DOI: 10.4310/jdg/1099587729

Abstract

We define a new spectrum for compact length spaces and Riemannian manifolds called the “covering spectrum” which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers δ>0 which identify the distinct δ covers of the space. We investigate the relationship between this covering spectrum, the length spectrum, the marked length spectrum and the Laplace spectrum. We analyze the behavior of the covering spectrum under Gromov–Hausdorff convergence and study its gap phenomenon.

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Christina Sormani. Guofang Wei. "The covering spectrum of a compact length space." J. Differential Geom. 67 (1) 35 - 77, May 2004. https://doi.org/10.4310/jdg/1099587729

Information

Published: May 2004
First available in Project Euclid: 4 November 2004

zbMATH: 1106.58025
MathSciNet: MR2153481
Digital Object Identifier: 10.4310/jdg/1099587729

Rights: Copyright © 2004 Lehigh University

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Vol.67 • No. 1 • May 2004
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