Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume
Name
stability.BrM.pdf
Description
Accepted version
Size
348.25 KB
Format
Adobe PDF
Checksum (MD5)
5cfc6a6e8554c97c55377ff19eadb294
Author(s)
Figalli, Alessio
Jerison, David
Date Issued
2017
Journal
Chinese Annals of Mathematics. Series B
Publisher
Springer Nature
Citation
Figalli, Alessio, and David Jerison. "Quantitative Stability of the Brunn-Minkowski Inequality for Sets of Equal Volume." Chinese Annals of Mathematics Series B 38 2 (2017): 393-412.
Version
Author's final manuscript
Abstract
© 2017, Fudan University and Springer-Verlag Berlin Heidelberg. The authors prove a quantitative stability result for the Brunn-Minkowski inequality on sets of equal volume: If |A| = |B| > 0 and |A + B|1/n = (2+δ)|A|1/n for some small δ, then, up to a translation, both A and B are close (in terms of δ) to a convex set K. Although this result was already proved by the authors in a previous paper, the present paper provides a more elementary proof that the authors believe has its own interest. Also, the result here provides a stronger estimate for the stability exponent than the previous result of the authors.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/S11401-017-1075-8
