Non UBC
DSpace
Livshyts, Galyna
2018-09-23T05:01:23Z
2018-03-26T17:11
In the recent years, a number of conjectures has appeared, concerning the improvement
of the inequalities of Brunn-Minkowski type under the additional assumptions of symmetry; this
includes the B-conjecture, the Gardner-Zvavitch conjecture of 2008, the Log-Brunn-Minkowski conjecture
of 2012, and some variants. The conjecture of Gardner and Zvavitch, also known as dimensional
Brunn-Minkowski conjecture, states that even log-concave measures in $\R^n$ are in fact $\frac{1}{n}$-
concave with respect to the addition of symmetric convex sets. In this talk we shall establish the
validity of the Gardner-Zvavitch conjecture asymptotically, and prove that the standard Gaussian measure
enjoys $\frac{0.37}{n}$ concavity with respect to centered convex sets. Some improvements to the case of
general log-concave measures shall be discussed as well. This is a joint work with A. Kolesnikov.
https://circle.library.ubc.ca/rest/handle/2429/67234?expand=metadata
27 minutes
video/mp4
Author affiliation: Georgia Institute of Technology
Banff (Alta.)
10.14288/1.0372139
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Faculty
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Functional analysis
Convex and discrete geometry
On the dimensional Brunn-Minkowski inequality
Moving Image
http://hdl.handle.net/2429/67234