论文标题
$ l_p $ -minkowski与超临界指数的问题
The $L_p$-Minkowski problem with super-critical exponents
论文作者
论文摘要
$ l_p $ -Minkowski问题涉及$ \ Mathbb {r}^{n+1} $中的封闭凸高空的存在。它扩展了经典的Minkowski问题，并包含了几种重要的几何和物理应用。在次临界情况下$ p> -n-1 $中已经获得了解决方案的存在，但是在超临界情况下，问题仍然广泛开放。在本文中，我们介绍了新的想法，以解决所有超临界指数的问题。我们证明中的关键成分是基于椭圆形拓扑空间的同源性的拓扑方法。
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 $p<-n-1$. In this paper, we introduce new ideas to solve the problem for all the super-critical exponents. A crucial ingredient in our proof is a topological method based on the calculation of the homology of a topological space of ellipsoids.
