A classification of $\operatorname{SL}(n)$ invariant valuations

By Monika Ludwig, Matthias Reitzner. 2010

149 citations recorded by the source corpus.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/3246e2ab4012558fafef06f033712deef452e442

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In Applied Mathematics

In Molecular Biology

Citations in the corpus

Functional Versions of Lp-Affine Surface Area and Entropy Inequalities (2014, unknown): “For convex bodies with the origin in their interiors, such upper semi-continuous valuations were characterized as Lp-affine surface areas in [30] and [31] which motivated us to call asλ(ψ) the Lλ-affine surface area of ψ.”
Relative entropy of cone measures and Lp centroid bodies (2009, background): “Lutwak and Zhang [39] generalized the notion of Binet ellipsoid and introduced the Lp centroid bodies defined by their support function hZp(K) as given in (1.4).”
The Hadwiger Theorem on Convex Functions, I (2020, background): “Interesting new valuations keep arising (see, for example, [8,24,31]) and see [1,2,4,6,7,21,22,29,32,35,36,39] for some recent classification results.”
An asymmetric affine Pólya–Szegö principle (2012, unknown): “, [10,15,35,38,46–55,57,58]).”
Cone-volume measure of general centered convex bodies (2016, unknown): “Reitzner [29], E.”
Sharp convex Lorentz–Sobolev inequalities (2011, unknown): “The set function ψ can be chosen as the integral affine surface area � p or other important geometric functionals of compact convex sets, in particular, valuations (see [3,28,29,37,39, 40 ]).”
The logarithmic Minkowski problem (2012, unknown): “[4], [19], [37], [38], [50], [51], [54], and [59].”
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).”
General affine surface areas (2009, background): “The Lp affine surface areas for p > 0 are special cases of the following family of affine surface areas introduced in [23].”