1 citations · 3 across the 9 of their papers we have counts for
10 papers
Localization of valuations and Alesker's irreducibility theorem
Georg C. Hofstätter, Jonas Knoerr
We provide a new proof of Alesker's Irreducibility Theorem. We first introduce a new localization technique for polynomial valuations on convex bodies, which we use to independentl…
Mixed Christoffel-Minkowski problems for bodies of revolution
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
The mixed Christoffel-Minkowski problem asks for necessary and sufficient conditions for a Borel measure on the Euclidean unit sphere to be the mixed area measure of some convex bo…
The Christoffel problem for the disk area measure
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
The mixed Christoffel problem asks for necessary and sufficient conditions for a Borel measure on the Euclidean unit sphere to be the mixed area measure of some convex bodies, all…
Affine Quermassintegrals and Even Minkowski Valuations
Georg C. Hofstätter, Philipp Kniefacz, Franz E. Schuster
It is shown that each continuous even Minkowski valuation on convex bodies of degree intertwining rigid motions is obtained from convolution of the th proj…
The Klain approach to zonal valuations
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
We show an analogue of the Klain-Schneider theorem for valuations that are invariant under rotations around a fixed axis, called zonal. Using this, we establish a new integral repr…
Busemann-Petty type problems on complex vector spaces
Simon Ellmeyer, Georg C. Hofstätter
Busemann-Petty type problems for the recently introduced complex projection, centroid and -intersection body operators are examined. Moreover, it is shown that, as their real…
Lefschetz operators on convex valuations
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
We investigate the action of Alesker's Lefschetz operators on translation invariant valuations on convex bodies. For scalar valued valuations, we describe this action on the level…
Convex valuations, from Whitney to Nash
Dmitry Faifman, Georg C. Hofstätter
We consider the Whitney problem for valuations: does a smooth -homogeneous translation-invariant valuation on exist that has given restrictions to a fixed family $…
Complex -Intersection Bodies
Simon Ellmeyer, Georg C. Hofstätter
Interpolating between the classic notions of intersection and polar centroid bodies, (real) -intersection bodies, for , play an important role in the dual -Brunn-…
Blaschke-Santaló inequalities for Minkowski and Asplund endomorphisms
Georg C. Hofstätter, Franz E. Schuster
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…