A family of maps with many small fibers

2014/02/12 by Alpert, Hannah, Guth, Larry
#53C23 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1402.2856

Abstract

The waist inequality states that for a continuous map from Sⁿ to R^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.

Related

• Waist of maps measured via Urysohn width
• The width-volume inequality
• Varieties of general type with small volumes
• Application of waist inequality to entropy and mean dimension
• Application of waist inequality to entropy and mean dimension: II