How to recognize convexity of a set from its marginals
Name
2016_Jerison_How to recognize.pdf
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192.54 KB
Format
Adobe PDF
Checksum (MD5)
68000086c30c33dc5d8ed0dcca241d0f
Author(s)
Figalli, Alessio
Jerison, David
Date Issued
June 2013
Journal
Journal of Functional Analysis
Publisher
Elsevier
Citation
Figalli, Alessio, and David Jerison. “How to Recognize Convexity of a Set from Its Marginals.” Journal of Functional Analysis 266, no. 3 (February 2014): 1685–1701.
Version
Author's final manuscript
Abstract
We investigate the regularity of the marginals onto hyperplanes for sets of finite perimeter. We prove, in particular, that if a set of finite perimeter has log-concave marginals onto a.e. hyperplane then the set is convex. Our proof relies on measuring the perimeter of a set through a Hilbertian fractional Sobolev norm, a fact that we believe has its own interest.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-NoDerivatives
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.jfa.2013.05.040
