Geometric Analysis Seminars——On the planar dual Minkowski problem
主 题: Geometric Analysis Seminars——On the planar dual Minkowski problem
报告人: Shibing Chen (The Australian National University)
时 间: 2017-11-08 16:00-17:00
地 点: Room 1418, Sciences Building No. 1
Abstract: In this talk, I will discuss our recent work on the planar dual Minkowski problem, proposed by Huang-Lutwak-Yang-Zhang (ACTA2016), without any symmetry assumptions. More precisely, given any $q>0$, and function $f$ on $S^1$, bounded by two positive constants, we show that there exists a convex body $\Omega$ in the plane, containing the origin in its interior, whose dual curvature measure has density $f$. In particular, if $f$ is smooth, then $\partial Omega$ is also smooth. Our method can be also applied if $f$ is a function of multi-variables.
This is based on a recent joint work with Qirui Li.
