Ellipsoids and matrix-valued valuations

By Monika Ludwig. 2003

214 citations recorded by the source corpus.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/b66b97090fb8ee5749a2b2a6ad46fec59a58539d

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In Applied Mathematics

In Discrete Mathematics and Combinatorics

Citations in the corpus

The logarithmic Minkowski problem (2012, unknown): “When p = 2, the measure S 2 ( K, · ) is called the quadratic surface area measure of K , which was studied in [42], [43], and [36].”
Volume inequalities for asymmetric Wulff shapes (2011, background): “In fact Ludwig [21] showed that the operators Γ−2 and Γ2 are the only linearly intertwining maps on convex bodies that satisfy the inclusionexclusion principle (see also [16, 22–24] for related results).”
Minkowski valuations intertwining the special linear group (2012, background): “, [24–26,29,30,35,37–39,56–58]).”
The log-Brunn-Minkowski inequality (2012, unknown): “[5,8–12,16,18,22–30,32–55,58,62–65,67–69]).”
Shadow systems of asymmetric Lp zonotopes (2013, unknown): “[9,12,21,23,26–30,32,35–37,44,46–48,51]).”
Valuations and Busemann{Petty Type Problems (2008, result): “For some of the more recent results, see [1,2,29,30,38,41].”
General $L_p$ affine isoperimetric inequalities (2008, result): “For some of the more recent results, see [1–4, 19–24].”
Volume Inequalities for Subspaces of L p (2004, unknown): “[7], [8], [9], [15], [16], [17], [22], [23], [24], [25], [26], [27], [28], [30], [29], [31], [32], [33], [34], [35], [39], [43], [44], [45], [46], [48]) motivated the search for a direct approach to establishing these reverse inequalities.”
Affine Moser–Trudinger and Morrey–Sobolev inequalities (2009, unknown): “, [12], [14], [27], [31], [32], [33] – [41], [44], [48] – [50]).”
The Hadwiger Theorem on Convex Functions, I (2020, background): “Interesting new valuations keep arising (see, for example, [8,21,28]) and see [1,2,4,6,7,18,19,26,29,32,33,36] for some recent classification results.”
R\'enyi Divergence and $L_p$-affine surface area for convex bodies (2011, unknown): “, [5], [7] - [11], [13], [14], [17] - [24], [26], [28], [31] - [34], [37], [38] - [46], [50]), is now a central part of modern convex geometry.”