On Mahler's conjecture for even s-concave functions in dimensions 1 and 2

Abstract

In this paper, we establish different sharp forms of Mahler's conjecture for $$-concave even functions in dimensions $$, for $$ and 2, for $$, thus generalizing our previous results in Fradelizi and Nakhle (Int. Math. Res. Not. 12 (2023), 10067–10097) on log-concave even functions in dimension 2, which corresponds to the case $$. The functional volume product of an even $$-concave function $$ is