The Centro-Affine Hadwiger Theorem

By Christoph Haberl, Lukas Parapatits. 2013

149 citations recorded by the source corpus.

All upper semicontinuous and SL(n) invariant valuations on convex bodies containing the origin in their interiors are completely classified. Each such valuation is shown to be a linear combination of the Euler characteristic, the volume, the volume of the polar body, and the recently discovered Orlicz surface areas.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/f76afdcbb4e9a9b0d3cc06372a3939c10d7f45cc

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In Applied Mathematics

Citations in the corpus

Cone-volume measure of general centered convex bodies (2016, unknown): “Parapatits [21,29] and the references within.”
The Spherical Convex Floating Body (2014, unknown): “Building on results of M. Ludwig and M. Reitzner [42], this result was recently considerably strengthened by C. Haberl and L. Parapatits [29].”
A homogeneous decomposition theorem for valuations on convex functions (2019, background): “Here strong structure and classification theorems have been established over the last seventy years (see [1, 2, 6, 7, 19–21, 28] for some recent results and [22, 23, 36] for information on the classical theory).”
The dual Orlicz–Brunn–Minkowski theory ☆ (2014, background): “) The new theory has already attracted considerable interest; see, for example, [2, 3, 4, 5, 21, 22, 25, 26, 39, 40, 41, 46].”
On the L dual Minkowski problem (2018, background): “See, for example, Alesker [1], Haberl [26], Haberl & Parapatits [28], Ludwig [42, 43, 45, 46], Ludwig & Reitzner [47], Schuster [59, 60], Schuster & Wannerer [61] and the references therein for important valuations in the theory of convex bodies.”
Minkowski valuations and generalized valuations (2015, background): “, [4, 9, 13, 31, 43]) and, more general, equivariant tensor valued valuations, where A = SymRn (see [3, 10, 35, 67]).”
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.”