158 citations · 341 across the 12 of their papers we have counts for
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Volume inequalities and additive maps of convex bodies
Franz E. Schuster
Analogues of the classical inequalities from the Brunn-Minkowski theory for rotation intertwining additive maps of convex bodies are developed. Analogues are also proved of inequal…
Rotation invariant Minkowski classes of convex bodies
Rolf Schneider, Franz E. Schuster
A Minkowski class is a closed subset of the space of convex bodies in Euclidean space Rn which is closed under Minkowski addition and non-negative dilatations. A convex body in Rn…
Rotation equivariant Minkowski valuations
Rolf Schneider, Franz E. Schuster
The projection body operator Π, which associates with every convex body in Euclidean space Rn its projection body, is a continuous valuation, it is invariant under translations and…
The Steiner Formula for Minkowski Valuations
Lukas Parapatits, Franz E. Schuster
A Steiner type formula for continuous translation invariant Minkowski valuations is established. In combination with a recent result on the symmetry of rigid motion invariant homog…
The Sine Transform of Isotropic Measures
Gabriel Maresch, Franz E. Schuster
Sharp isoperimetric inequalities for the sine transform of even isotropic measures are established. The corresponding reverse inequalities are obtained in an asymptotically optimal…
GL(n) contravariant Minkowski valuations
Franz E. Schuster, Thomas Wannerer
A complete classification of all continuous GL(n) contravariant Minkowski valuations is established. As an application we present a family of sharp isoperimetric inequalities for s…