Uniqueness and Continuity of the Solution to Lp Dual Minkowski Problem

作者：Wang, Hejun; Zhou, Jiazu^*

来源：Communications in Mathematics and Statistics, 2024.

DOI：10.1007/s40304-023-00374-2

• L(p )dual Minkowski problem
• L(p )dual curvature
• Minkowski-type inequlity
• Uniqueness
• Continuity

Lutwak et al. (Adv Math 329:85-132, 2018) introduced the L-p dual curvature measure that unifies several other geometric measures in dual Brunn-Minkowski theory and Brunn-Minkowski theory. Motivated by works in Lutwak et al. (Adv Math 329:85-132, 2018), we consider the uniqueness and continuity of the solution to the L-p dual Minkowski problem. To extend the important work (Theorem A) of LYZ to the case for general convex bodies, we establish some new Minkowski-type inequalities which are closely related to the optimization problem associated with the L-p dual Minkowski problem. When q<p, the uniqueness of the solution to the L-p dual Minkowski problem for general convex bodies is obtained. Moreover, we obtain the continuity of the solution to the L-p dual Minkowski problem for convex bodies.

• 单位
  西南大学