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# Larry Guth : Area-contracting maps between rectangles

The k-dilation of a map measures how much the map stretches k-dimensional volumes. The 1-dilation is the usual Lipschitz constant. We consider the problem of finding the smallest k-dilation among all degree 1 maps from one rectangle to another rectangle. (These are n-dimensional rectangles.) In general the linear map is far from optimal.

**Category**: Geometry and Topology**Duration**: 01:34:43**Date**: October 23, 2007 at 4:25 PM**Views**: 151-
**Tags:**seminar, Geometry/topology Seminar

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