4 papers
Smooth solutions to the chord log-Minkowski problem
Jinrong Hu, Yong Huang, Jian Lu
In integral geometry generalized with Aleksandrov's variational theory, Lutwak-Xi-Yang-Zhang [Comm. Pure Appl. Math. 77 (2024)] recently opened the door to researching the cone-cho…
A flow approach to the monotonicity of shape functionals
Yong Huang, Qinfeng Li, Shuangquan Xie +1
We develop a geometric flow framework to investigate two classical shape functionals: the torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. First, by construc…
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…
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…