Stable quotients of periodic minimal surfaces
Stable quotients of periodic minimal surfaces
复制标题
周期极小曲面的稳定商
DOI：
10.4310/cag.1994.v2.n3.a4
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发表时间：
1994
影响因子：
0.7
通讯作者：
Chad Schoen
中科院分区：
文献类型：
--
作者：
Marty Ross;Chad Schoen
设L_c_R是一个离散格，并设x：M -* R/！/是一个完整的和连接的最低限度的沉浸。设x是稳定的，M有有限亏格，证明了若秩L = 1或2，则x（M）是平面、螺旋面或Scherk曲面的商.证明结合了最小曲面理论与代数几何的技术。
Let L c R be a discrete lattice and suppose x : M —* R/!/ is a complete and connected minimal immersion. Assuming that x is stable and M has finite genus we prove that if rank L = 1 or 2 then x(M) is a quotient of the plane, the helicoid or a Scherk's surface. The proof combines minimal surface theory with techniques from algebraic geometry.