GL(n) contravariant Minkowski valuations

By Franz E. Schuster, Thomas Wannerer. 2012

104 citations recorded by the source corpus.

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 such valuations which generalize the classical Petty projection inequality.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5e848bbf51c709787008132b1794f5d0547f55e9

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In Applied Mathematics

In Mathematical Physics

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.”
Valuations on Sobolev spaces (2012, background): “See [25, 30, 47, 48] for information on the classical theory of valuations on convex bodies and [1, 2, 3, 4, 5, 9, 16, 21, 20, 22, 23, 33, 34, 35, 38, 39, 51, 53, 54, 58] for some of the more recent results.”
The Spherical Convex Floating Body (2014, unknown): “In particular, the affine isoperimetric inequality implies the Blaschke-Santaló inequality and it proved to be the key ingredient in the solution of many problems, see e.g. the book by R. J. Gardner [22] and also [13] [21] [30] [40] [46] [67] [75] [78].”
Existence of solutions to the even dual Minkowski problem (2018, methodology): “Valuations have been the objects of many recent works, see, for example, Haberl [28], Haberl & Parapatits [29], Ludwig [37, 39], Ludwig & Reitzner [40], Schuster [57, 58], Schuster & Wannerer [59] and the references therein.”
Functional Versions of Lp-Affine Surface Area and Entropy Inequalities (2014, unknown): “The L p -aﬃne surface area and its related inequalities play a major role in convex and diﬀerential geometry [2, 22, 24, 30, 31, 34, 43, 45, 47, 48, 50, 51, 52].”
The dual Minkowski problem for negative indices (2017, background): “See, e.g., Haberl [19], Haberl & Ludwig [20] ,Haberl & Parapatits [21,22], Ludwig [27,28], Ludwig & Reitzner [29], Schuster [39, 40], Schuster & Wannerer [41] and the references therein for important valuations and their characterizations in the theory of convex bodies.”
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].”
Difference bodies in complex vector spaces (2012, background): “Some results on Minkowksi valuations not described in this paper can be found, for instance, in [18, 19, 21, 32, 33, 42, 43, 45].”