New Kähler metric on quasifuchsian space and its curvature properties

Notes on the Schwarzian tensor and measured foliations at infinity of quasifuchsian manifolds

The boundary at infinity of a quasifuchsian hyperbolic manifold is equiped with a holomorphic quadratic differential. Its horizontal measured foliation $f$ can be interpreted as the natural analog of the measured bending lamination on the boundary of the convex core. This analogy leads to a number of questions. We provide a variation formula for the renormalized volume in terms of the extremal length $\ext(f)$ of $f$, and an upper bound on $\ext(f)$. We then describe two extensions of the holomorphic quadratic differential at infinity, both valid in higher dimensions. One is in terms of Poinca…

正标量曲率4维流形的去奇异化

Desingularizing positive scalar curvature 4-manifolds

本文利用显式psc零配边及Lock–Viaclovsky的标量平坦Kähler ALE曲面，证明闭3维psc流形配边群平凡，并据此建立可扩大4维流形上奇异psc度量的不存在性及低正则渐近平坦4维流形的正质量定理。

反德西特时空中具有指定诱导度量的凸曲面

Convex surfaces with prescribed induced metrics in anti-de Sitter spacetimes

本文证明了在亏格至少为2的闭曲面上，对任意曲率小于-1的度量与双曲度量，存在唯一的拟富克斯反德西特时空，使其包含诱导度量同痕于给定度量的过去凸柯西曲面。