论文标题
单位磁盘的第一个$ p $ widths
The first $p$-widths of the unit disk
论文作者
论文摘要
在具有非空凸边界的紧凑型2个manifolds上，我们证明了具有自由边界和$ \ Mathbb {z} _2 $的积分1-varifolds $ v $的规律性结果 - 在小annuli中最小化。这种规律性说，$ v $是一个免费的边界有限的测量网络。接下来，使用该规律性，我们计算了单位闭合球$ b^2的第一个$ p $ widths，$ p = 1，。 。 。 ，4。$
On compact 2-manifolds with non-empty convex boundary, we prove a regularity result for integral 1-varifolds $V$ that are stationary with free boundary and $\mathbb{Z}_2$-almost minimizing in small annuli. That regularity says that $V$ is a free boundary finite geodesic network. Next, using that regularity, we compute the first $p$-widths of the unit closed ball $B^2,$ for $p=1, . . . , 4.$
