论文标题
球形度量和圆锥形奇点的表面几何分解
Geometric decompositions of surfaces with spherical metric and conical singularities
论文作者
论文摘要
我们证明，任何具有恒定正曲率和圆锥形奇点的紧凑表面都可以分解为标准形状的不可还原成分，沿连接圆锥形奇异性的地球弧线粘合。这是具有圆锥形奇异性平面的几何三角形的球形类似物。不可还原的组件不仅包括球形三角形，还包括其他有趣的球形多边形。特别是，我们介绍了\ textit {半球凹形多边形}的类别，它们是没有对角线的球形多边形的，并且可以任意复杂。最后，我们在球形表面的设置中介绍了核心作为几何不变的概念。我们使用它来证明总锥形角度至少$（10G-10+5N）2π$的球形表面的还原结果。
We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. This is a spherical analog of the geometric triangulations for flat surfaces with conical singularities. The irreducible components include not only spherical triangles but also other interesting spherical polygons. In particular, we present the class of \textit{half-spherical concave polygons} that are spherical polygons without diagonals and that can be arbitrarily complicated. Finally, we introduce the notion of core as a geometric invariant in the settings of spherical surfaces. We use it to prove a reducibily result for spherical surfaces with a total conical angle at least $(10g-10+5n)2π$.
