A characterization of spherical polyhedron surfaces

Geometric decompositions of surfaces with spherical metric and conical singularities

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.…

Surface subgroups from homology

Let G be a word-hyperbolic group, obtained as a graph of free groups amalgamated along cyclic subgroups. If H_2(G;Q) is nonzero, then G contains a closed hyperbolic surface subgroup. Moreover, the unit ball of the Gromov-Thurston norm on H_2(G;R) is a finite-sided rational polyhedron.

曲面上的球面正交环模式与修正组合全测地曲率

Spherical orthogonal ring patterns on surfaces and modified combinatorial total geodesic curvatures

研究闭曲面上球面正交环模式的刚性问题，通过修正Nie的组合全测地曲率并利用变分原理，证明了满足特定条件的闭曲面上球面正交环模式的刚性。

球面锥面之间极小拉格朗日微分同胚的刚性

Rigidity of minimal Lagrangian diffeomorphisms between spherical cone surfaces

本文证明具有锥奇点的闭球面之间的极小拉格朗日微分同胚必为等距映射，并将Liebmann刚性定理推广到常正高斯曲率闭曲面的分支浸入情形。

二面角球面曲面的模空间与测度叶状结构

Moduli Space of Dihedral Spherical Surfaces and Measured Foliations

本文研究二面角球面曲面，通过定义一对横向测度叶状结构来完全刻画该类曲面，并引入几何分解与形变方法，最终确定给定锥角和拓扑类型下模空间的维数。

Finite presentations for spherical/braid twist groups from decorated marked surfaces

We give a finite presentation for the braid twist group of a decorated surface. If the decorated surface arises from a triangulated marked surface without punctures, we obtain a finite presentation for the spherical twist group of the associated 3-Calabi-Yau triangulated category. The motivation/application is that the result will be used to show that the (principal component of) space of stability conditions on the 3-Calabi-Yau category is simply connected in the sequel.

通过球状对象质量得到的K3曲面上的稳定性条件

Stability conditions on K3 surfaces via mass of spherical objects

该研究证明K3曲面上的稳定性条件由球状对象质量经自然$\mathbb{C}$-作用唯一确定，受相关紧化构造提议启发，还构造了与球状丛相关的松弛稳定性条件，推进了稳定性流形紧化研究。

Decorated marked surfaces: spherical twists versus braid twists

We are interested in the 3-Calabi-Yau categories $\mathcal{D}$ arising from quivers with potential associated to a triangulated marked surface $\mathbf{S}$ (without punctures). We prove that the spherical twist group ST of $\mathcal{D}$ is isomorphic to a subgroup (generated by braid twists) of the mapping class group of the decorated marked surface $\mathbf{S}_{\bigtriangleup}$. Here $\mathbf{S}_{\bigtriangleup}$ is the surface obtained from $\mathbf{S}$ by decorating with a set of decorated points, where the number of points equals the number of triangles in any triangulations of $\mathbf{S}…