Surface bodies and p-affine surface area

By C. Schütt, Elisabeth M. Werner. 2004

205 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/0c465d26bb30f5b71c7d6a8deab2a6b279e0ef11

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In Applied Mathematics

In Geometry and Topology

In Molecular Biology

Citations in the corpus

Dual Orlicz–Brunn–Minkowski theory: Dual Orlicz Lϕ affine and geominimal surface areas (2014, background): “These affine invariants are very useful in applications, see [15, 17, 21, 22, 23, 35, 40, 43, 44] among others.”
Functional Versions of Lp-Affine Surface Area and Entropy Inequalities (2014, unknown): “…we recall that for p ∈ R , p (cid:54) = − n , the L p -aﬃne surface area of a convex body K in R n with the origin in its interior is deﬁned [26, 33, 47] by Here, N K ( x ) is the outer unit normal at x ∈ ∂K , µ K is the usual surface area measure on ∂K and κ K ( x ) is the Gauss curvature at x .”
Dual Orlicz-Brunn-Minkowski theory (2014, unknown): “See [4,5,7,22,39,41,45,51,52] for additional references.”
Orlicz centroid bodies (2010, unknown): “, [1–9,17– 23,26–32,34–44,46–48,54,56,57,59,62].”
General affine surface areas (2009, methodology): “For p −n, Lp affine surface area was defined by Schütt and Werner [39] using (2).”
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.”
R\'enyi Divergence and $L_p$-affine surface area for convex bodies (2011, methodology): “1 was used in [40] to give geometric interpretations of the L p-affine surface area.”
The Spherical Convex Floating Body (2014, unknown): “A variant of the convex floating body provided a geometric interpretation of L p -affine surface area, see C. Schütt and E. Werner [73].”
Valuations and Surface Area Measures (2014, unknown): “[7, 10,17,18,22,25,28,29,36,42–45]).”
Centro-Affine Invariants for Smooth Convex Bodies (2010, background): “Originally introduced for p > 0, see also [19], Meyer-Werner considered Ωp for−n < p < 0 and Schütt-Werner for p on (−∞,∞), respectively, [38], [46].”
Lp John Ellipsoids (2005, background): “If in addition to containing the origin in its interior, the body K has a curvature function, then fpðK; Þ:S 1 ! R, the Lp-curvature function of K, is de2ned by fpðK; Þ 1⁄4 h(1) p K fðK; Þ: Since its introduction in the mid 90 s, Lp curvature (and the functionals it gives rise to) have attracted inc”
A classification of $\operatorname{SL}(n)$ invariant valuations (2010, unknown): “Geometric interpretations of Lp affine surface areas are obtained in [17], [49], [55], [63], and an application of Lp affine surface areas to partial differential equations is given in [40].”
Orlicz projection bodies (2010, unknown): “[2–8,14–19,22–28,30–43,49,51, 52,54,55].”