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15 May 2016 Families of short cycles on Riemannian surfaces
Yevgeny Liokumovich
Duke Math. J. 165(7): 1363-1379 (15 May 2016). DOI: 10.1215/00127094-3450208

Abstract

Let M be a closed Riemannian surface of genus g. We construct a family of 1-cycles on M that represents a nontrivial element of the kth homology group of the space of cycles and such that the mass of each cycle is bounded above by Cmax {k,g}Area(M). This result is optimal up to a multiplicative constant.

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Yevgeny Liokumovich. "Families of short cycles on Riemannian surfaces." Duke Math. J. 165 (7) 1363 - 1379, 15 May 2016. https://doi.org/10.1215/00127094-3450208

Information

Received: 15 November 2014; Revised: 16 August 2015; Published: 15 May 2016
First available in Project Euclid: 5 February 2016

zbMATH: 1341.53072
MathSciNet: MR3498868
Digital Object Identifier: 10.1215/00127094-3450208

Subjects:
Primary: 53C23
Secondary: 30F10

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 7 • 15 May 2016
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