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Uniqueness of a smooth convex body with uniform cone volume measure in the neighborhood of a ball

Connections for Women: geometry and probability in high dimensions August 17, 2017 - August 18, 2017

August 17, 2017 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Galyna Livshyts (Georgia Institute of Technology)
Tags/Keywords
  • cone volume measure

  • hausdorff neighborhood

  • log-brunn-minkowski

Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

3-Livshyts

Abstract

We prove that in every n-dimensional there exists a constant c=c(n)>0 so that in the c(n)-neighborhood of a ball, the only convex body with uniform cone volume measure is the ball. The goal of the talk will be to give an insight into some analytic aspects of the Log-Brunn-Minkowski and Log-Minkowski conjectures made by Boroczky, Lutwak, Yang and Zhang. This talk is based on the joint papers with Colesanti, Marsiglietti and Colesanti.

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Video/Audio Files

3-Livshyts

H.264 Video 3-Livshiyts.mp4 343 MB video/mp4 rtsp://videos.msri.org/data/000/029/211/original/3-Livshiyts.mp4 Download
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