391 citations · 694 across the 7 of their papers we have counts for
7 papers
Chord Measures in Integral Geometry and Their Minkowski Problems
Erwin Lutwak, Dongmeng Xi, Deane Yang +1
To the families of geometric measures of convex bodies (the area measures of Aleksandrov-Fenchel-Jessen, the curvature measures of Federer, and the recently discovered dual curvatu…
Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
Yong Huang, Erwin Lutwak, Deane Yang +1
A longstanding question in the dual Brunn-Minkowski theory is what are the dual analogues of Federer's curvature measures for convex bodies. The answer to this is provided. This le…
The Logarithmic Minkowski Problem
Károly J. Böröczky, Erwin Lutwak, Deane Yang +1
In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the u…
The dual Minkowski problem for symmetric convex bodies
Károly Böröczky, Erwin Lutwak, Deane Yang +2
The dual Minkowski problem for even data asks what are the necessary and sufficient conditions on an even prescribed measure on the unit sphere for it to be the -th dual curvatu…
A countable set of directions is sufficient for Steiner symmetrization
Gabriele Bianchi, Daniel A. Klain, Erwin Lutwak +2
A countable dense set of directions is sufficient for Steiner symmetrization, but the order of directions matters.
Volume Inequalities for Isotropic Measures
Erwin Lutwak, Deane Yang, Gaoyong Zhang
A direct approach to Ball's simplex inequality is presented. This approach, which does not use the Brascamp-Lieb inequality, also gives Barthe's characterization of the simplex for…