391 citations · 768 across the 12 of their papers we have counts for
12 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…
Minkowski Problems for Geometric Measures
Yong Huang, Deane Yang, Gaoyang Zhzng
This paper describes the theory of Minkowski problems for geometric measures in convex geometric analysis. The theory goes back to Minkowski and Aleksandrov and has been developed…
The -Minkowski problem for
Gabriele Bianchi, Károly J. Böröczky, Andrea Colesanti +1
Chou and Wang's existence result for the -Minkowski problem on for and an absolutely continuous measure is discussed and extended to more…
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…