Projection bodies in complex vector spaces

By Judit Abardia, A. Bernig. 2011

111 citations recorded by the source corpus.

The space of Minkowski valuations on an m-dimensional complex vector space which are continuous, translation invariant and contravariant under the complex special linear group is explicitly described. Each valuation with these properties is shown to satisfy geometric inequalities of the Brunn–Minkowski, Aleksandrov–Fenchel and Minkowski type.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/ffa61f1daca24d59a940cea9059c8dc2cae9800c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Thomas Wannerer
2. A. Bernig
3. Franz E. Schuster
4. Daniel Hug
5. Judit Abardia
6. Semyon Alesker
7. Monika Ludwig
8. Yiming Zhao

In Astronomy and Astrophysics

1. Thomas Wannerer
2. A. Bernig
3. Daniel Hug
4. Franz E. Schuster
5. Judit Abardia
6. Monika Ludwig

Citations in the corpus

• Kinematic formulas for tensor valuations (2014, background): “We refer to [1, 2, 24, 31, 44, 46] to cite just a few papers in this direction.”
• Minkowski valuations and generalized valuations (2015, background): “In a more recent influential article, Ludwig [41] coined the name Minkowski valuations for such maps and started a line of research concerned with the classification of Minkowski valuations intertwining linear transformations, see [1, 2, 30, 40, 42, 61, 65].”
• Harmonic Analysis of Translation Invariant Valuations (2010, background): “Its variants and generalizations have been used extensively for establishing geometric inequalities related to convex and star body valued valuations (see [GZ], [GrZ], [HS], [Lu1,2,4,5], [LuYZ1], [LuYZ2], [LuZ], [S2] and section 7). Complex versions of the projection body were recently studied in [ ”
• Difference bodies in complex vector spaces (2012, result): “In [1] a complex version of this result was shown.”
• Algebraic Integral Geometry (2010, background): “V) in Definition 2.1. It is easy to see that µ(K) = Kdefines a valuation. More interesting examples are the intersection body operator (defined on a subset of K(V)) and the projection body operator. See [42, 43, 56, 3] for more information. If A= Sym∗ V, the space of symmetric tensors over V, then A-va”