49 citations · 217 across the 14 of their papers we have counts for
6 papers · 1 filter
Explicit solutions to Christoffel-Minkowski problems and Hessian equations under rotational symmetries
Fabian Mussnig, Jacopo Ulivelli
An explicit solution to the Christoffel-Minkowski problem for convex bodies of revolution is presented. The conditions on the prescribed measure involve only first moments over sph…
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-…
Valuations on Convex Bodies and Functions
Monika Ludwig, Fabian Mussnig
An introduction to geometric valuation theory is given. The focus is on classification results for invariant and rigid motion invariant valuations on convex…
A homogeneous decomposition theorem for valuations on convex functions
A. Colesanti, M. Ludwig, F. Mussnig
The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation inva…
Valuations on Log-Concave Functions
Fabian Mussnig
A classification of and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced lev…