论文标题
完整最小表面的高斯图的空间
The space of Gauss maps of complete minimal surfaces
论文作者
论文摘要
共形最小沉浸在$ \ Mathbb r^3 $中的共形最小沉浸式的高斯地图是$ m $的meromorphic功能。在本文中，我们证明了高斯地图分配，即在其高斯地图上采用完整的共形最小沉浸式$ m \至\ mathbb r^3 $，是一种serre纤维。然后，我们在$ m $上确定Meromormorphic函数空间的同质类型，这是完整的完整保形最小沉浸的高斯地图，并表明它与从$ M $到2-Sphere的所有连续地图的同型均值类型相同。我们获得了共同化的高斯浸入式$ m \ to \ mathbb r^n $的类似结果，用于任意$ n \ geq 3 $。
The Gauss map of a conformal minimal immersion of an open Riemann surface $M$ into $\mathbb R^3$ is a meromorphic function on $M$. In this paper, we prove that the Gauss map assignment, taking a full conformal minimal immersion $M\to\mathbb R^3$ to its Gauss map, is a Serre fibration. We then determine the homotopy type of the space of meromorphic functions on $M$ that are the Gauss map of a complete full conformal minimal immersion, and show that it is the same as the homotopy type of the space of all continuous maps from $M$ to the 2-sphere. We obtain analogous results for the generalised Gauss map of conformal minimal immersions $M\to\mathbb R^n$ for arbitrary $n\geq 3$.
