1 citations · 2 across the 6 of their papers we have counts for
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The Riesz -energy of log-concave functions and related Minkowski problem
Niufa Fang, Deping Ye, Zengle Zhang
We calculate the first order variation of the Riesz -energy of a log-concave function with respect to the Asplund sum. Such a variational formula induces the Riesz -energ…
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…
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…
Geometry of log-concave functions: the Asplund sum and the Minkowski problem
Niufa Fang, Sudan Xing, Deping Ye
The aim of this paper is to develop a basic framework of the theory for the geometry of log-concave functions, which can be viewed as a functional "lifting" of the Brun…
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].