论文标题
凸锥中的加权相对等级不等式
A weighted relative isoperimetric inequality in convex cones
论文作者
论文摘要
凸锥中的加权相对等级不等式是通过Monge-Ampere方程获得的。该方法改善了文献中的几种不平等现象，例如cabre-ros--ros-oton-serra的常数。应用是在对数凸密度密度概括的上下文中给出的，并由钱伯斯解决：在$α-$均匀的情况下（$α> 0 $）（$α> 0 $），凹密度（mod翻译），以原点为中心，与锥相结合的圆锥体与锥体相交的质量非常小于量表的体重计的体重量非常轻微，重量表的体重计的重量表则是一个重量级的体重计。特别是，如果将锥体视为$ \ {x_n> 0 \} $，反映了密度，则与$ \ {x_n> 0 \} $相交的球相交（mod translations）在$ \ mathbb {r}^n $模拟的情况下，在$ \ \ \ n $ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {x x n = 0时，
A weighted relative isoperimetric inequality in convex cones is obtained via the Monge-Ampere equation. The method improves several inequalities in the literature, e.g. constants in a theorem of Cabre--Ros--Oton--Serra. Applications are given in the context of a generalization of the log-convex density conjecture due to Brakke and resolved by Chambers: in the case of $α-$homogeneous ($α>0$), concave densities, (mod translations) balls centered at the origin and intersected with the cone are proved to uniquely minimize the weighted perimeter with a weighted mass constraint. In particular, if the cone is taken to be $\{x_n>0\}$, reflecting the density, balls intersected with $\{x_n>0\}$ remain (mod translations) unique minimizers in the $\mathbb{R}^n$ analog in the case when the density vanishes on $\{x_n=0\}$.
