The Riesz $\alpha$-energy of log-concave functions and related Minkowski problem

Niufa Fang, Deping Ye, Zengle Zhang

We calculate the first order variation of the Riesz $\alpha$-energy of a log-concave function $f$ with respect to the Asplund sum. Such a variational formula induces the Riesz $\alpha$-energ…