Regularity theory for $2$-dimensional almost minimal currents I: Lipschitz approximation
Regularity theory for $2$-dimensional almost minimal currents I: Lipschitz approximation
复制标题
$2$维几乎最小电流的正则理论 I：Lipschitz 近似
DOI：
10.1090/tran/6995
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
L. Spolaor
中科院分区：
文献类型：
--
作者：
Camillo De Lellis;E. Spadaro;L. Spolaor
我们构造Lipschitz $Q$值函数，仔细近似积分电流时，他们的圆柱形的过剩是小的，他们几乎是最小化在一个合适的意义。这一结果是在随后的两个工作证明了以下三类的奇异集的离散性$2$维积分电流：面积最小化黎曼流形，半校准和球形截面的$3$维面积最小化锥。
We construct Lipschitz $Q$-valued functions which approximate carefully integral currents when their cylindrical excess is small and they are almost minimizing in a suitable sense. This result is used in two subsequent works to prove the discreteness of the singular set for the following three classes of $2$-dimensional integral currents: area minimizing in Riemannian manifolds, semicalibrated and spherical cross sections of $3$-dimensional area minimizing cones.