Elliptic isometries of the manifold of definite positive real matrices with the trace metric

Special elliptic isometries, relative SU(2,1)-character varieties, and bendings

We study relations between special elliptic isometries in the complex hyperbolic plane. Relations of lengths 2, 3, and 4 are fully classified. Some relative SU(2,1)-character varieties of the quadruply punctured sphere are described and applied to the study of length 5 relations.

The length of PU(2,1) relative to special elliptic isometries with fixed parameter

Generalizing the involution length of the complex hyperbolic plane, we obtain that the $α$-length of $\mathrm{PU}(2,1)$ is $4$, that is, every element of $\mathrm{PU}(2,1)$ can be decomposed as the product of at most $4$ special elliptic isometries with parameter $α$. We also describe the isometries that can be written as the product of $2$ or $3$ such special elliptic isometries.

椭圆三维流形的等距

Isometries of elliptic 3-manifolds

常正曲率的闭三维流形很久以前就被Seifert和Threlfall分类了。利用已知的关于正交群O（4）的信息，我们计算了它们的全等距群Isom（M），确定了哪些椭圆3-流形允许在所有等距下不变的Seifert纤维化，并验证了Isom（M）到Diff（M）的包含是路径分量上的双射.

Differential properties of spaces of symmetric real matrices

We study the differential geometric properties of the manifold of non-singular symmetric real matrices endowed with the trace metric; in case of positive definite matrices we describe the full group of isometries

Stability of elliptic Harnack inequality

We prove that the elliptic Harnack inequality (on a manifold, graph, or suitably regular metric measure space) is stable under bounded perturbations, as well as rough isometries.

Riemann-Roch isometries in the non-compact orbifold setting

We generalize work of Deligne and Gillet-Soulé on a Riemann-Roch type isometry, to the case of the trivial sheaf on cusp compactifications of Riemann surfaces $Γ\backslash\mathbb{H}$, for $Γ\subset PSL_{2}(\mathbb{R})$ a fuchsian group of the first kind, equipped with the Poincaré metric. This metric is singular at cusps and elliptic fixed points, and the results of Deligne and Gillet-Soulé do not apply to this setting. Our theorem relates the determinant of cohomology of the trivial sheaf, with an explicit Quillen type metric in terms of the Selberg zeta function of $Γ$, to a metrized version…