Volume inequalities and additive maps of convex bodies
By Franz E. Schuster. 2006
72 citations recorded by the source corpus.
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 inequalities from the dual Brunn-Minkowski theory for intertwining additive maps of star bodies. These inequalities provide generalizations of results for projection and intersection bodies. As a corollary, a new Brunn-Minkowski inequality is obtained for the volume of polar projection bodies.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/f92f9f93a3cac14d21f173e006f8a5978d7e81c8
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In Applied Mathematics
- Franz E. Schuster
- Rolf Schneider
- Monika Ludwig
- Yiming Zhao
- Thomas Wannerer
- Christoph Haberl
- A. Bernig
- Judit Abardia
Citations in the corpus
- Rotation equivariant Minkowski valuations (2012, background): “0. The case of valuations homogeneous of degree n 1, called Blaschke Minkowski homomorphisms, was investigated recently by the second author in [29, 30 ].”
- Valuations and Busemann{Petty Type Problems (2008, background): “In [62,63] the author investigated continuous maps Φ : K → K called Blaschke–Minkowski homomorphisms, which are SO(n) equivariant and satisfy”
- Crofton Measures and Minkowski Valuations (2010, methodology): “Moreover, the author obtained in [46] an array of geometric inequalities for the intrinsic volumes of derived (non-trivial) Minkowski valuations Ψi.”