曲面的Brylinski β函数

同轴层的Brylinski beta函数

The Brylinski beta function of a coaxial layer

本文将Brylinski beta函数推广到欧氏空间子流形上的同轴层分布，证明其可亚纯延拓至全复平面且仅有简单极点，并对空间曲线情形用曲率和挠率计算了部分留数。

The Brylinski beta function of a double layer

An analogue of Brylinski's knot beta function is defined for a compactly supported (Schwartz) distribution $T$ on $d$-dimensional Euclidean space. This is a holomorphic function on a right half-plane. If $T$ is a (uniform) double-layer on a compact smooth hypersurface, then the beta function has an analytic continuation to the complex plane as a meromorphic function, and the residues are integrals of invariants of the second fundamental form. The first few residues are computed when $d=2$ and $d=3$.

Riesz 能量与流形的 magnitude 不变量

Riesz energies and the magnitude of manifolds

本文揭示了闭流形上 magnitude 不变量与 Brylinski beta 函数的精确联系，并通过初等证明和伪微分分析统一了其几何信息，还推广到 p-adic 整数情形。

H^{2,2}中的多项式极大曲面与球面多边形

Polynomial Maximal Surfaces in H^{2,2} and Spherical Polygons

研究伪双曲空间中具有类光多边形渐近边界的完备极大曲面模空间，引入转动不变量分类其连通分支，通过多项式给出模空间的几何参数化，关联Hitchin分支的相关研究。