The Lp Shephard problem on entropy of log-concave functions
In this paper,we introduce the Lp Shephard problem on entropy of log-concave functions,a comparison problem:whether Πpf≤Πpg implies that Ent(f)≥ Ent(g),for 1 ≤ p＜n,and Ent(f)≤ Ent(g),for n＜p,where Πpf is the Lp projection body of a log-concave function f.Our results give a partial answer to this problem.
the Lp Shephard problemlog-concave functionsLp projection bodiesentropy
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