The $L_p$-Minkowski problem with super-critical exponents
Qiang Guang, Qirui Li, Xu‐Jia Wang · arXiv (Cornell University) · 2022
The $L_p$-Minkowski problem deals with the existence of closed convex hypersurfaces in $\mathbb{R}^{n+1}$ with prescribed $p$-area measures. It extends the classical Minkowski problem and embraces several important geometric and physical applications. The Existence of solutions has been obtained in the sub-critical case $p>-n-1$, but the problem remains widely open in the super-critical case $p