Duke Mathematical Journal
- Duke Math. J.
- Volume 165, Number 7 (2016), 1363-1379.
Families of short cycles on Riemannian surfaces
Let be a closed Riemannian surface of genus . We construct a family of 1-cycles on 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 . This result is optimal up to a multiplicative constant.
Duke Math. J., Volume 165, Number 7 (2016), 1363-1379.
Received: 15 November 2014
Revised: 16 August 2015
First available in Project Euclid: 5 February 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 30F10: Compact Riemann surfaces and uniformization [See also 14H15, 32G15]
Liokumovich, Yevgeny. Families of short cycles on Riemannian surfaces. Duke Math. J. 165 (2016), no. 7, 1363--1379. doi:10.1215/00127094-3450208. https://projecteuclid.org/euclid.dmj/1454683425