3 papers
math.MG2025
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…
math.MG2025
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…
math.MG2025
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…