On the Lp affine isoperimetric inequalities

By Wuyang Yu, Gangsong Leng. 2011

192 citations recorded by the source corpus.

Subfields: Applied Mathematics, Pharmacology

View Paper: https://www.semanticscholar.org/paper/69d1a1bcad00d078da6034e53e236595e6962518

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In Applied Mathematics

In Pharmacology

Citations in the corpus

Minkowski valuations and generalized valuations (2015, unknown): “, [2, 11, 32, 44–46, 61]).”
A volume inequality for polar bodies (2010, unknown): “, [8–13, 15, 21–38, 41, 44,45,47–49,51]).”
GL(n) contravariant Minkowski valuations (2012, unknown): “(For important recent generalizations, see [25, 28].”
Projection bodies in complex vector spaces (2011, background): “For additional information and recent results on projection bodies see, for example, [14, 19, 23, 33, 34, 35, 36, 43, 51].”
Crofton Measures and Minkowski Valuations (2010, background): “(For important recent related results on Lp projection bodies, see [37–39]).”
OPERATIONS BETWEEN SETS IN GEOMETRY (2012, unknown): “See, for example, [9], [22], [23], [29], [30], [31], [32], [33], and [34].”
More on logarithmic sums of convex bodies (2014, background): “[31] [32] [33] [34] [35]), much less seem to be known for 0 ≤ p < 1.”
THE ORLICZ-BRUNN-MINKOWSKI THEORY: A GENERAL FRAMEWORK, ADDITIONS, AND INEQUALITIES (2013, unknown): “See, for example, [4], [13], [14], [21], [22], [23], [24], [26], and [35].”
Fisher information and matrix-valued valuations (2011, background): “The proof of the theorem is based on the intriguing connection between information theory and the L2 Brunn Minkowski Theory (see [12,13,17,23, 35–42,47,48] for information on the Lp Brunn Minkowski Theory).”
An asymmetric affine Pólya–Szegö principle (2012, unknown): “, [10,15,35,38,46–54,56,57]).”
The $L_p$-Aleksandrov problem for $L_p$-integral curvature (2018, methodology): “In [11, 21, 37, 39, 54] affine Sobolev inequalities were obtained by using the solution of the Minkowski problem and the Lp-Minkowski problem (together with Lpaffine isoperimetric inequalities from [36, 20]).”
SL(n)-Contravariant $L_p$-Minkowski Valuations (2014, background): “The symmetric Lp-projection body was first introduced by Lutwak, Yang and Zhang in [31].”
A probabilistic take on isoperimetric-type inequalities (2012, background): “For star-shaped bodiesK ⊂ R the latter inequality, together with the equality conditions, is proved in [23]; see [8] for an alternate proof.”
Anisotropic fractional perimeters (2013, unknown): “In recent years, centroid bodies have found powerful extensions within the L Brunn Minkowski theory [26–28,30], the asymmetric L Brunn Minkowski theory [21,23] and the Orlicz Brunn Minkowski theory [29].”