The degeneration of convex RP^2 structures on surfaces

带边界双曲曲面沿调和映射射线的一致退化

Uniform degeneration of hyperbolic surfaces with boundary along harmonic map rays

本文证明带边界双曲曲面沿调和映射射线退化时，其万有覆盖重标度距离一致收敛到垂直测度叶状结构的交数，并在 Gromov-Hausdorff 意义下收敛到对偶 R-树，从而确定其 Thurston 边界极限。

Degeneration of Heegaard genus, a survey

We survey known (and unknown) results about the behavior of Heegaard genus of 3-manifolds constructed via various gluings. The constructions we consider are (1) gluing together two 3-manifolds with incompressible boundary, (2) gluing together the boundary components of surface times I, and (3) gluing a handlebody to the boundary of a 3-manifold. We detail those cases in which it is known when the Heegaard genus is less than what is expected after gluing.

k-正曲面群表示的退化

Degenerations of k-positive surface group representations

该研究引入与Hitchin表示有诸多共性的k-正曲面群表示，分析其退化规律，并提出正比表示的一般极限定理作为核心工具。

关于极小次数曲面退化的 Galois 覆盖

On the Galois covers of degenerations of surfaces of minimal degree

本文研究复射影空间中极小次数曲面的 Galois 覆盖拓扑，并证明 n≥5 时这些覆盖均为单连通的一般类型曲面。

非阿基米德希尔伯特几何与实希尔伯特几何的退化

Non-Archimedean Hilbert geometry and degenerations of real Hilbert geometries

本文发展了有序值域上的希尔伯特几何理论，证明缩放实希尔伯特几何的超极限与非阿基米德希尔伯特空间等距，并描述了非阿基米德有界多胞形的希尔伯特度量，从而得到实多胞形缩放度量的 Gromov-Hausdorff 极限。

Length spectra and degeneration of flat metrics

In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to get a boundary for the space of flat metrics. The geometric interpretation is that flat metrics degenerate to "mixed structures" on the surface: part flat metric and part measured foliation.

del Pezzo 曲面退化中的 Wahl 奇点

Wahl singularities in degenerations of del Pezzo surfaces

本文通过引入带标记的 del Pezzo Wahl 链，刻画了次数为 $1 \leq \ell \leq 9$ 的 del Pezzo 曲面退化中的所有 Wahl 奇点，并揭示了其与伪加权射影平面的对应关系及在低次曲面中的应用。

仅具有有理奇点的复射影平面的退化

Degenerations of the complex projective plane with only rational singularities

在瓦尔猜想成立的前提下，对仅具有理奇点的复射影平面正规退化进行分类，包括马内蒂和哈金 - 普罗霍罗夫分类的由马尔可夫方程控制的曲面，以及含四个非对数典范奇点的六个新退化。

Skein代数的退化与量子迹

Degenerations Of Skein Algebras And Quantum Traces

本文提出统一Roger-Yang与带状态skein代数的LRY skein代数，通过量子迹和修改的Dehn-Thurston坐标证明其整环、退化、维数、Noether性及有限生成性质。

KIAS关于退化的辛几何方面的讲座

KIAS Lectures on Symplectic Aspects of Degenerations

本文是作者2019年在韩国高等研究院研讨会上所作三场关于退化辛几何方面讲座的讲义，聚焦循环商曲面奇点，经小修正后发布至arXiv作永久留存，为2016-2019年相关思考的阐述性内容。

The Hilbert area of inscribed triangles and quadrilaterals

Hilbert volume is an invariant of real projective geometry. Polygons inscribed in polygons are considered for the real projective plane. The correspondence between Fock-Goncharov and Cartesian coordinates is examined. Degeneration and Hilbert area of inscribed quadrilaterals are analyzed. A microlocal condition is developed for bounded Hilbert area under degeneration. The condition is applied to give a sequence of strictly convex domains with bounded Hilbert area and divergent Goldman parameters.

Multiple Saddle Connections on Flat Surfaces and Principal Boundary of the Moduli Spaces of Quadratic Differentials

We describe typical degenerations of quadratic differentials thus describing ``generic cusps'' of the moduli space of meromorphic quadratic differentials with at most simple poles. The part of the boundary of the moduli space which does not arise from ``generic'' degenerations is often negligible in problems involving information on compactification of the moduli space. However, even for a typical degeneration one may have several short loops on the Riemann surface which shrink simultaneously. We explain this phenomenon, describe all rigid configurations of short loops, present a detailed desc…

膨胀曲面上的闭测地线

Closed geodesics in dilation surfaces

本研究证明了任意膨胀曲面上闭测地线的方向在圆周上稠密，通过研究模空间中泰希米勒流作用下膨胀曲面Delaunay三角剖分的退化完成证明，推进了膨胀曲面几何的相关研究。

On real anti-bicanonical curves with one double point on the 4-th real Hirzebruch surface

We list up all the candidates for the real isotopy types of real anti-bicanonical curves with one real nondegenerate double point on the 4-th real Hirzebruch surface RF_4 by enumerating the connected components of the moduli space of real 2-elementary K3 surfaces of type (S,θ)=((3,1,1), -id). We also list up all the candidates for the non-increasing simplest degenerations of real nonsingular anti-bicanonical curves on RF_4. We find an interesting correspondence between the real isotopy types of real anti-bicanonical curves with one real nondegenerate double point on RF_4 and the non-increasing…