A family of maps with many small fibers

Author(s)
Alpert, Hannah; Guth, Lawrence
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Abstract
The waist inequality states that for a continuous map from S[superscript n] < to ℝ [superscript q], not all fibers can have small (n - q)-dimensional volume. We construct maps for which most fibers have small (n - q)-dimensional volume and all fibers have bounded (n - q)-dimensional volume. Keywords: waist inequality; isoperimetric inequality
Date issued
2014-09
URI
http://hdl.handle.net/1721.1/115580
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Journal of Topology and Analysis
Publisher
World Scientific Publishing
Citation
Alpert, Hannah and Larry Guth. “A Family of Maps with Many Small Fibers.” Journal of Topology and Analysis 7, 1 (March 2015): 73–79 © 2015 World Scientific Publishing Company
Version: Original manuscript
ISSN
1793-5253
1793-7167
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