This is an announcement for the paper "Orlicz Affine Isoperimetric Inequalities for Functions" by Umut Caglar and Deping Ye.
Abstract: In this paper, we develop basic theory for the Orlicz affine surface areas for log-concave and $s$-concave functions. Our definitions were motivated by recently developed 1) Orlicz affine and geominimal surface areas for convex bodies, and 2) $L_p$ affine surface areas for log-concave and $s$-concave functions. We prove some basic properties for these newly introduced functional affine invariants, and establish related functional affine isoperimetric inequalities as well as generalized functional Blaschke-Santal'o and inverse Santal'o inequalities.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A20, 53A15, 46B, 60B
Submitted from: deping.ye@gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.02974
or