Star body valued valuations

By Christoph Haberl. 2009

77 citations recorded by the source corpus.

Subfields: Applied Mathematics, Pharmacology

View Paper: https://www.semanticscholar.org/paper/797946a7d7aac156f07b24af773b67560f10c8a6

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In Applied Mathematics

In Pharmacology

Citations in the corpus

Minkowski Areas and Valuations (2010, background): “Many of these affine functions on convex bodies can be completely characterized by their invariance and valuation properties (see, for example, [22, 23, 24, 33, 34, 35, 36, 37, 38, 40]).”
The even Orlicz-Minkowski problem (2010, unknown): “[1–5, 7–10, 12, 13, 15–22, 25–39, 41–44, 47, 49, 50, 52–55, 58, 60–63, 65–68]).”
General affine surface areas (2009, unknown): “We follow Schütt [42] (see also [14]) and work with the decompositions ∂(K ∪ L) = ( ∂K ∩ ∂L ) ∪ ( ∂K ∩ L ) ∪ ( ∂L ∩K ) , ∂(K ∩ L) = ( ∂K ∩ ∂L ) ∪ ( ∂K ∩ intL ) ∪ ( ∂L ∩ intK ) , ∂K = ( ∂K ∩ ∂L ) ∪ ( ∂K ∩ L ) ∪ ( ∂K ∩ intL ) , ∂L = ( ∂K ∩ ∂L ) ∪ ( ∂L ∩K ) ∪ ( ∂L ∩ intK ) ,”
Fisher information and matrix-valued valuations (2011, result): “See [24, 27] for information on the classical theory of valuations on convex sets and [1–5,9,11,16,19–22,28– 31, 33, 34, 43–45] for some of the more recent results.”
The log-Brunn-Minkowski inequality (2012, unknown): “[5,8–12,16,18,22–30,32–55,58,62–65,67–69]).”
A classification of $\operatorname{SL}(n)$ invariant valuations (2010, background): “Since then investigations of valuations have been an active and prominent part of mathematics (see [1]–[8], [16], [19], [20], [24], [25], [31]–[34], and [53] for some of the more recent results).”
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.”
Crofton Measures and Minkowski Valuations (2010, background): “Schneider [42] in the 1970s, but only through the recent seminal work of Ludwig [29, 31] classications of convex and star body valued valuations have become the focus of increased attention, see [ 21 , 22, 24, 32, 44, 47].”
$\mathrm{GL}(n)$ contravariant Minkowski valuations (2012, unknown): “, [9–11, 21, 38].”
Minkowski valuations intertwining the special linear group (2012, background): “, [24–26,29,30,35,37–39,56–58]).”