论文标题
$ \ ell^1 $ norm中的双重气泡问题的基本证明
An elementary proof for the Double Bubble problem in $\ell^1$ norm
论文作者
论文摘要
我们研究了$ \ Mathbb {r}^2 $上的$ \ ell_1 $ norm的外围的双气泡问题。我们通过直接比较一个参数化集合的小家族，为任何体积比参数的存在最小化$ 0 <α\ le1 $提供了基本证明。通过对该家族的简单分析，我们获得了Morgan等人1998中发现的最小化形状。
We study the double bubble problem with perimeter taken with respect to the $\ell_1$ norm on $\mathbb{R}^2$. We give an elementary proof for the existence of minimizing sets for any volume ratio parameter $0<α\le1$ by direct comparison to a small family of parameterized sets. By simple analysis on this family we obtain the minimizing shapes found in Morgan et al 1998.
