论文标题
CANTOR END的最小表面的Calabi-Yau问题
The Calabi-Yau problem for minimal surfaces with Cantor ends
论文作者
论文摘要
我们表明，每个连接的紧凑型或边界的Riemann表面都包含一个cantor套件，其补充允许完整的同条最小沉浸在$ \ mathbb r^3 $中，并带有有界图像。类似的结果使全体形态沉浸至至少$ 2 $的任何复杂的层次中，全态无效的沉浸在$ \ mathbb c^n $中，带有$ n \ ge 3 $，用于holomorphic legendrian legendrian浸入任意的复杂接触中，以超级或超级临时或自我态度，并以任何自我为代表。
We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in $\mathbb R^3$ with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least $2$, for holomorphic null immersions into $\mathbb C^n$ with $n\ge 3$, for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for superminimal immersions in any self-dual or anti-self-dual Einstein four-manifold.
