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Strengthened inequalities for the mean width and the -norm of origin symmetric convex bodies
Károly J. Böröczky, Ferenc Fodor, Daniel Hug
Barthe, Schechtman and Schmuckenschläger proved that the cube maximizes the mean width of symmetric convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the bo…
Additive kinematic formulas for convex functions
Daniel Hug, Fabian Mussnig, Jacopo Ulivelli
We prove a functional version of the additive kinematic formula as an application of the Hadwiger theorem on convex functions together with a Kubota-type formula for mixed Monge-Am…
Kubota-type formulas and supports of mixed measures
Daniel Hug, Fabian Mussnig, Jacopo Ulivelli
Kubota's integral formula expresses the intrinsic volumes of a convex body as averages over its projections onto linear subspaces. In this work, we introduce a new class of Kubota-…
The support of mixed area measures involving a new class of convex bodies
Daniel Hug, Paul A. Reichert
Mixed volumes in -dimensional Euclidean space are functionals of -tuples of convex bodies . The Alexandrov--Fenchel inequalities are fundamental inequ…
Extremizers of the Alexandrov--Fenchel inequality within a new class of convex bodies
Daniel Hug, Paul A. Reichert
Mixed volumes in -dimensional Euclidean space are functionals of -tuples consisting of convex bodies . The Alexandrov--Fenchel inequalities are fundam…