A characterization of Lp intersection bodies

By Christoph Haberl, Monika Ludwig. 2006

162 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Graphics and Computer-Aided Design, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c025cfd005f7bc703c9d49149b71747d59216eb5

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In Applied Mathematics

In Computer Graphics and Computer-Aided Design

In Geometry and Topology

Citations in the corpus

Valuations and Busemann{Petty Type Problems (2008, background): “In recent years the investigations of convex and star body valued valuations gained momentum through a series of articles by Ludwig [37,39,40], see also [23].”
A new proof of the Orlicz Busemann-Petty centroid inequality (2011, unknown): “, [1]–[5], [7]–[24], [29] and the references therein.”
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]).”
Star body valued valuations (2009, background): “The operators Γ p are closely related to the generalized MinkowskiFunk transform [40] and are the asymmetric Lp analogs of the intersection body operator for negative p; see [12], [13].”
General $L_p$ affine isoperimetric inequalities (2008, background): “Since their introduction Lp moment bodies have become the focus of intense study, see e.g., [6, 8, 12, 15, 16, 21, 30, 51] and the noted paper [36].”
Valuations and Surface Area Measures (2014, unknown): “[2–6, 9, 13–15, 20–25, 34, 39–41]).”
Minkowski valuations intertwining the special linear group (2012, background): “, [24–26,29,30,35,37–39,56–58]).”
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]).”
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 Centro-Affine Hadwiger Theorem (2013, background): “With the aid of elementary moves [46], one can show that the last property forces μ to vanish on Pn o (see [26]).”
Centro-Affine Invariants for Smooth Convex Bodies (2010, background): “The new view brought a renewed focus on the class of convex bodies (compact convex sets) containing the origin in their interior on which many affine invariants and many affineinvariant inequalities were derived, [6], [7], [12]–[15], [23], [31]–[35], [54]– [56].”
Dual Orlicz-Brunn-Minkowski theory (2014, background): “If K is a convex polytope in R with the origin in its interior, then this Lp intersection body is consistent with the Lp intersection body in [21].”
$\mathrm{GL}(n)$ contravariant Minkowski valuations (2012, unknown): “, [9–11, 21, 38].”
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.”
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.”