106 citations · 138 across the 8 of their papers we have counts for
8 papers · 1 filter
On the planar Gaussian-Minkowski problem
Shibing Chen, Shengnan Hu, Weiru Liu +1
The current work focuses on the Gaussian-Minkowski problem in dimension 2. In particular, we show that if the Gaussian surface area measure is proportional to the spherical Lebesgu…
The Chord Minkowski problem in a critical interval
Lujun Guo, Dongmeng Xi, Yiming Zhao
Chord measures and chord measures were recently introduced by Lutwak-Xi-Yang-Zhang by establishing a variational formula regarding a family of fundamental integral geometric…
Dual curvature measures for log-concave functions
Yong Huang, Jiaqian Liu, Dongmeng Xi +1
We introduce dual curvature measures for log-concave functions, which in the case of characteristic functions recover the dual curvature measures for convex bodies introduced by Hu…
The Minkowski problem in the Gaussian probability space
Yong Huang, Dongmeng Xi, Yiming Zhao
The Minkowski problem in Gaussian probability space is studied in this paper. In addition to providing an existence result on a Gaussian-volume-normalized version of this problem,…
The Aleksandrov problem for origin-symmetric polytopes
Yiming Zhao
The Aleksandrov integral curvature and its corresponding characterization problem---the Aleksandrov problem---were recently introduced by Huang, Lutwak, Yang, and Zhang…
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…
The dual Minkowski problem for negative indices
Yiming Zhao
Recently, the duals of Federer's curvature measures, called dual curvature measures, were discovered by Huang, Lutwak, Yang, and Zhang (ACTA, 2016). In the same paper, they posed t…
On Affine Surface Area and Curvature Measures
Yiming Zhao
The relationship between affine surface area and curvature measures is investigated. As a result, a new representation of the existing notion of affine surface area dep…