Projection bodies and valuations

By Monika Ludwig. 2002

191 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/37b8147758e7d5d21abe6d3d8c12e56ffa620d2f

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

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]).”
Divergence for s-concave and log concave functions (2013, background): “, [19]- [23], [29], [30], [34]- [48], [58], [62]- [67], [69], [72]), this theory is now a central part of modern convex geometry.”
Sharp convex Lorentz–Sobolev inequalities (2011, unknown): “Deﬁne the convexiﬁed Choquet integral, ψ (cid:104) f (cid:105) , of a function f with respect to ψ as The set function ψ can be chosen as the integral aﬃne surface area Φ p or other important geometric functionals of compact convex sets, in particular, valuations (see [3, 28, 29, 37, 38, 40]).”
The log-Brunn-Minkowski inequality (2012, unknown): “[5,8–12,16,18,22–30,32–55,58,62–65,67–69]).”
Orlicz projection bodies (2010, background): “Work of Ludwig [31] (see also [28]) showed that the known Lp extension of the projection operator considered in [39] is only one of a family of natural Lp extensions of their classical counterpart.”
Harmonic Analysis of Translation Invariant Valuations (2010, background): “For the special role of the map Π in the theory of valuations we refer to [32].”
Rotation equivariant Minkowski valuations (2012, background): “2], extending a previous result from [13], is the following characterization of the projection body operator.”
Minkowski valuations intertwining the special linear group (2012, background): “, [24–26,29,30,35,37–39,56–58]).”
GL(n) equivariant Minkowski valuations (2013, background): “The proof is similar to the SL(n) contravariant case treated in [41] and is based on ideas and techniques developed by Ludwig in [23].”
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], [53] for some of the more recent results).”
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].”
General $L_p$ affine isoperimetric inequalities (2008, background): “Ludwig’s classification results in [21] were in fact formulated with a different parametrization of the families c1 · Π + p +p c2 · Π − p and c1 · M + p +p c2 · M − p .”
Convolutions and multiplier transformations of convex bodies (2007, background): “For further information on valuations of this type see [15] and [16].”
Crofton Measures and Minkowski Valuations (2010, background): “In a different line of research, with a similar far reaching impact on the theory of valuations, Ludwig [29, 31, 32] first obtained characterizations of convex and star body valued valuations which are compatible with nondegenerate linear transformations, see also [22].”
GL(n) contravariant Minkowski valuations (2012, background): “The following theorem is an example of the numerous results obtained there: Theorem 1 (Ludwig [20]).”