Functional Geominimal Surface Area and Its Related Affine Isoperimetric Inequality - Niufa Fang; Jin Yang (Journal of Function Spaces)
The first variation of the total mass of log-concave functions was studied by Colesanti and Fragalà, which includes the Lp mixed volume of convex bodies. Using Colesanti and Fragalà’s first variation formula, we define the geominimal surface area for log-concave functions, and its related affine isoperimetric inequality is also established.