Lp John Ellipsoids

By Erwin Lutwak, Deane Yang, Gaoyong Zhang. 2005

169 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/1801d139e2766a41e0ad10b880a6cc0a9b83ca58

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yiming Zhao
2. Deping Ye
3. K. Boroczky
4. Deane Yang
5. Gaoyong Zhang
6. Erwin Lutwak
7. Yong Huang
8. Sudan Xing

In Computer Graphics and Computer-Aided Design

1. Manuel Weberndorfer
2. Franz E. Schuster
3. Ge Xiong
4. Du Zou
5. Marc Troyanov
6. V. Matveev
7. Deane Yang
8. Gaoyong Zhang

Citations in the corpus

• Affine images of isotropic measures (2015, background): “2) allows us to rewrite a basic question posed in [57] as follows: Problem 8.”
• The Dual Orlicz–Minkowski Problem (2017, background): “, [24, 31, 34, 39, 40, 48, 54]), the Lp Minkowski problem for p ≥ 1 is closely related to optimization problems involving the Lp mixed volume of convex bodies; this can be seen intuitively from the equality characterization of the Lp Minkowski inequality for the Lp mixed volume.”
• Dual Orlicz-Brunn-Minkowski theory (2014, unknown): “theory has been developed (see [20,31,33,38,42,56]).”
• Orlicz–John ellipsoids (2014, methodology): “In [38], it is proved that limp→∞ EpK = E∞K.”
• The Binet-Legendre Metric in Finsler Geometry (2011, methodology): “, Note that beside the John metric and the Binet-Legendre metric, we could use other procedures that associate a scalar product (or an ellipsoid) to a given convex body, such as the one considered in [41, 46, 51, 58, 59]. However, none of these constructions would give a metric with the desired prop”
• 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]).”
• Shadow systems of asymmetric Lp zonotopes (2013, unknown): “[9,12,21,23,26–30,32,35–37,44,46–48,51]).”
• Necessary subspace concentration conditions for the even dual Minkowski problem (2017, background): “al Minkowski problem as well as the logarithmic Minkowski problem. The cone-volume measure for convex bodies has been studied extensively over the last few years in many different contexts, see, e.g., [4, 5, 10, 11, 12, 23, 25, 27, 28, 29, 30, 31, 34, 35, 39, 40, 41, 42, 43, 44, 47, 51, 55, 56]. One ”
• The log-Brunn-Minkowski inequality (2012, background): “We need the normalized L p -mixed volume V̄ p (K, L), which was first defined in [43],”
• 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].”
• Volume inequalities for asymmetric Wulff shapes (2011, methodology): “In Section 6 we show how Theorems 1 and 2 directly imply a number of reverse isoperimetric inequalities (including all equality conditions) obtained by Ball [1, 2], Barthe [4] and Lutwak, Yang, Zhang [29, 31, 32].”
• Volume inequalities for isotropic measures (2006, background): “, [710,13-27,29-32,34,35,37]) none of the machinery of the theory is used.”