TY - ELEC
AU - Livshyts, Galyna
PY - 2018
TI - On the dimensional Brunn-Minkowski inequality
LA - eng
M3 - Moving Image
AB - 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.
N2 - 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.
UR - https://open.library.ubc.ca/collections/48630/items/1.0372139
ER - End of Reference