5 papers
An affine isoperimetric inequality for log-concave functions
Zengle Zhang, Jiazu Zhou
The authors gave an affine isoperimetric inequality \cite{LYZ2010} that gives a lower bound for the volume of a polar body and the equality holds if and only if the body is a simpl…
Dual curvature measures on convex functions and associated Minkowski problems
Niufa Fang, Jiazu Zhou
In this paper, the -th dual curvature measure is extended to convex functions and the associated Minkowski problem is posed. A special case includes the -th dual curvature me…
Uniqueness and continuity of the solution to dual Minkowski problem
Hejun Wang, Jiazu Zhou
Lutwak, Yang and Zhang \cite{LYZ2018} introduced the dual curvature measure that unifies several other geometric measures in dual Brunn-Minkowski theory and Brunn- Minkowski…
The Busemann-Petty problem on entropy of log-concave functions
Niufa Fang, Jiazu Zhou
The Busemann-Petty problem asks whether symmetric convex bodies in the Euclidean space with smaller central hyperplane sections necessarily have smaller volume. The…
Notes on the functional LYZ ellipsoid
Niufa Fang, Jiazu Zhou
We define the functional LYZ ellipsoid of log-concave functions. Then we give notes appended to [6].