A new ellipsoid associated with convex bodies

By Erwin Lutwak, Deane Yang, Gaoyong Zhang. 2000

235 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/f1ed5efaa4fc29ed9f8338cba28486e031a92089

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. Monika Ludwig
2. Yiming Zhao
3. Franz E. Schuster
4. Christoph Haberl
5. Deane Yang
6. Gaoyong Zhang
7. Erwin Lutwak
8. Deping Ye

In Geometry and Topology

1. Monika Ludwig
2. Franz E. Schuster
3. Yiming Zhao
4. Christoph Haberl
5. Deane Yang
6. Gaoyong Zhang
7. Erwin Lutwak
8. A. Bernig

In Molecular Biology

1. Monika Ludwig
2. Christoph Haberl
3. Deane Yang
4. Gaoyong Zhang
5. Franz E. Schuster
6. Erwin Lutwak
7. Elisabeth M. Werner
8. Manuel Weberndorfer

Citations in the corpus

• Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems (2016, unknown): “The L p Brunn-Minkowski theory is an extension of the classical Brunn-Minkowski theory, see [40, 47, 51, 54, 56, 57, 60, 63, 73].”
• Crofton Measures and Minkowski Valuations (2010, background): “(For important recent related results on Lp projection bodies, see [37–39]).”
• 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, background): “Sharp volume estimates for origin-symmetric Wulff shapes and their polars determined by even functions and isotropic measures (clearly, they are f -centered) can easily be deduced from previous work of Lutwak, Yang, and Zhang [29], see Section 3.”
• R\'enyi Divergence and $L_p$-affine surface area for convex bodies (2011, background): “[24,26,27,29] established further connections between convexity and information theory.”
• The Cramer-Rao inequality for star bodies (2002, methodology): “If the body K is convex, then this definition agrees with formula (5) and therefore with the original definition given in [26].”
• Fisher information and matrix-valued valuations (2011, methodology): “Lutwak, Yang, and Zhang [37] introduced a new ellipsoid associated with convex sets and showed in [39] that this LYZ ellipsoid corresponds to the Fisher information ellipsoid defined by the Fisher information matrix.”
• An asymmetric affine Pólya–Szegö principle (2012, background): “In this article we establish a new affine Pólya–Szegö type inequality which strengthens and directly implies the affine Pólya–Szegö principle of Cianchi, Lutwak, Yang, and Zhang.”