6 papers
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…
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…
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 $…
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…