It is shown that each monotone Minkowski endomorphism of convex bodies gives rise to an
isoperimetric inequality, which directly implies the classical Urysohn inequality. Among this …

This paper is dedicated to study the sine version of polar bodies and establish the L p-sine
Blaschke-Santaló inequality for the L p-sine centroid body. The L p-sine centroid body Λ p K …

This article delves into the L p Minkowski problem within the framework of generalized
Gaussian probability space. This type of probability space was initially introduced in …

Complex affine isoperimetric inequalities | SpringerLink Skip to main content Advertisement
SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Calculus of …

We introduce a family of general L p-moments of a continuous function with compact support
on R n and prove their associated L k, p moment-entropy inequalities. We show that these …

It is shown that for any sufficiently regular even Minkowski valuation Φ which is
homogeneous and intertwines rigid motions, there exists a neighborhood of the unit ball …

A family of sharp L^ p L p Sobolev inequalities is established by averaging the length of i-
dimensional projections of the gradient of a function. Moreover, it is shown that each of these …

The Petty projection inequality for sets of finite perimeter is proved. Our approach is based
on Steiner symmetrization. Neither the affine Sobolev inequality nor the functional …

A complete classification of all zonal, continuous, and translation invariant valuations on
convex bodies is established. The valuations obtained are expressed as principal value …

It is shown that for any sufficiently regular even Minkowski valuation Φ which is
homogeneous and intertwines rigid motions, and for any convex body K in a smooth …