亏格一多面体曲面，环面上二次微分空间和Laplacian行列式

任意亏格的紧致多面体曲面与Laplacian行列式

Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians

紧致多面体曲面（或等价地，紧致黎曼曲面与共形平坦圆锥度量）的任意亏格。在给出了一个简短的自包含的调查，他们的基本谱特性，我们研究了zeta正则行列式的拉普拉斯算子作为一个功能上的模空间这些表面。给出了该行列式的一个显式表达式。

Polyhedral approximation by Lagrangian and isotropic tori

We prove that every smoothly immersed 2-torus of $\mathbb{R}^4$ can be approximated, in the C0-sense, by immersed polyhedral Lagrangian tori. In the case of a smoothly immersed (resp. embedded) Lagrangian torus of $\mathbb{R}^4$, the surface can be approximated in the C1-sense by immersed (resp. embedded) polyhedral Lagrangian tori. Similar statements are proved for isotropic 2-tori of $\mathbb{R}^{2n}$.

高亏格多面体曲面上拉普拉斯算子行列式的变分公式

Variational formulas for determinant of Laplacian on higher genus polyhedral surface

该研究针对亏格不小于1的黎曼曲面上Friedrichs拉普拉斯算子的ζ-正则化行列式，推导了其在共形类内关于锥点和锥角的变分公式，积分后得到含模依赖因子的显式表达式，并指出该因子可通过与平凡和乐情形的已知公式对比计算。

Determinant of Laplacian on tori of constant positive curvature with one conical point

We find an explicit expression for the zeta-regularized determinant of (the Friedrichs extension) of the Laplacian on a compact Riemann surface of genus one with conformal metric of curvature $1$ having a single conical singularity of angle $4π$.

Metrics and compactifications of Teichmüller spaces of flat tori

Using the identification of the symmetric space $\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)$ with the Teichmüller space of flat $n$-tori of unit volume, we explore several metrics and compactifications of these spaces, drawing inspiration both from Teichmüller theory and symmetric spaces. We define and study analogs of the Thurston, Teichmüller, and Weil-Petersson metrics. We show the Teichmüller metric is a symmetrization of the Thurston metric, which is a polyhedral Finsler metric, and the Weil-Petersson metric is the Riemannian metric of $\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)$ as a symmetr…

透镜空间行列式

Lens space determinants

本文对齐次三维透镜空间上的算子行列式作了进一步的分析，重点是数值分析，以便能处理大质量场的拉普拉斯算子。也简要地考虑了多面体投影。研究了对应于平坦连接的扭曲场，并计算了行列式的示例。扭转循环量足以确定任何因子的任何扭转的循环量。本文给出了球对称热力学的一个应用。对非齐次透镜空间作了一些计算，并对高维作了评述，还讨论了最小耦合问题。