arXiv subjects

Yunhui Wu

Publications and source records attributed to Yunhui Wu.

41 records · Page 3Linked to original sources

arXiv2015

On the Weil-Petersson curvature of the moduli space of Riemann surfaces of large genus

Let $S_g$ be a closed surface of genus $g$ and $\mathbb{M}_g$ be the moduli space of $S_g$ endowed with the Weil-Petersson metric. In this paper we investigate the Weil-Petersson curvatures of $\mathbb{M}_g$ for large genus $g$. First, we study the asymptotic behavior of the extremal Weil-Petersson holomorphic sectional curvatures at certain thick surfaces in $\mathbb{M}_g$ as $g \to \infty$. Then we prove two curvature properties on the whole space $\mathbb{M}_g$ as $g\to \infty$ in a probabilistic way.

math.DG↗

arXiv2015

Scalar curvatures of Hermitian metrics on the moduli space of Riemann surfaces

In this article we show that any finite cover of the moduli space of closed Riemann surfaces of $g$ genus with $g\geq 2$ does not admit any complete finite-volume Hermitian metric of non-negative scalar curvature. Moreover, we also show that the total mass of the scalar curvature of any almost Hermitian metric, which is equivalent to the Teichmüller metric, on any finite cover of the moduli space is negative provided that the scalar curvature is bounded from below.

math.DG↗

arXiv2015

The Riemannian Sectional Curvature Operator Of The Weil-Petersson Metric and Its Application

Fix a number $g>1$, let $S$ be a close surface of genus $g$, and $Teich(S)$ be the Teichmüller space of $S$ endowed with the Weil-Petersson metric. In this paper we show that the Riemannian sectional curvature operator of $Teich(S)$ is non-positive definite. As an application we show that any twist harmonic map from rank-one hyperbolic spaces $H_{Q,m}=Sp(m,1)/Sp(m)\cdot Sp(1)$ or $H_{O,2}=F_{4}^{-20}/SO(9)$ into $Teich(S)$ is a constant.

math.DG↗

arXiv2013

Fundamental groups of finite volume, bounded negatively curved 4-manifolds are not 3-manifold groups

We study noncompact, complete, finite volume, Riemannian 4-manifolds $M$ with sectional curvature $-1<K<0$. We prove that $π_1 M$ cannot be a 3-manifold group. A classical theorem of Gromov says that $M$ is homeomorphic to the interior of a compact manifold $\M$ with boundary $\partial\barM$. We show that for each $π_1$-injective boundary component $C$ of $\M$, the map $i_*$ induced by inclusion $i\colon C\rightarrow \M$ has infinite index image $i_*(π_1 C)$ in $π_1 \M$. We also prove that $M$ cannot be homotoped to be contained in $\partial\M$.

math.GT↗

arXiv2013

Parabolic isometries of visible CAT(0) spaces and metrics on moduli space

We show that the translation length of any parabolic isometry on a complete semi-uniformly visible CAT(0) space is always zero. As a consequence, we will classify the isometries on visible CAT(0) spaces in terms of translation lengths. We will also show that the moduli space $\mathbb{M}(S_{g,n})$ of surface $S_{g,n}$ of $g$ genus with $n$ punctures admits no complete visible CAT(0) Riemannian metric if $3g+n\geq 5$, which answers the Brock-Farb-McMullen question in the visible case.

math.GT↗