158 citations · 341 across the 12 of their papers we have counts for
27 papers
Radon Transforms of Projection Functions and Aleksandrov-Fenchel Inequalities
Leo Brauner, Oscar Ortega-Moreno, Franz E. Schuster
The Radon transforms on Grassmannians define two families of geometric operators on convex bodies when applied to their projection functions. On the one hand, these are Minkowski's…
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…
Fixed points of Minkowski valuations
Oscar Ortega-Moreno, Franz E. Schuster
It is shown that for any sufficiently regular even Minkowski valuation which is homogeneous and intertwines rigid motions, there exists a neighborhood of the unit ball, where b…
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…
Sharp Sobolev inequalities via projection averages
Philipp Kniefacz, Franz E. Schuster
A family of sharp Sobolev inequalities is established by averaging the length of -dimensional projections of the gradient of a function. Moreover, it is shown that each of…
Lutwak-Petty projection inequalities for Minkowski valuations and their duals
Astrid Berg, Franz E. Schuster
Lutwak's volume inequalities for polar projection bodies of all orders are generalized to polarizations of Minkowski valuations generated by even, zonal measures on the Euclidean u…