Related papers: Parabolic bundles and spherical metrics

Let $G/H$ be a Riemannian homogeneous space. For an orthogonal representation $\phi$ of $H$ on the Euclidean space $\mathbb{R}^{k+1}$, there corresponds the vector bundle $E=G\times_{\phi}\mathbb{R}^{k+1} \to G/H$ with fiberwise inner…

We discuss the constant $\sigma_{2}$ problem for conic 4-spheres. Based on earlier works of Chang-Han-Yang and Han-Li-Teixeira, we are able to find a necessary condition for the existence problem. In particular, when the condition is sharp,…

The notion of flat $\lambda$-connections as the interpolation of usual flat connections and Higgs fields was suggested by Deligne and further studied by Simpson. Mochizuki established the Kobayashi--Hitchin-type theorem for $\lambda$-flat…

In a previous paper [BTF21] the authors employed the fiber join construction of Yamazaki [Yam99] together with the admissible construction of Apostolov, Calderbank, Gauduchon, and T{\o}nnesen-Friedman [ACGTF08a] to construct new extremal…

We construct complete Riemannian metrics to show that the total space of tangent bundles of orientable closed surfaces (except torus) admits complete uniformly PSC-metrics. It gives a partial positive answer to one of Gromov's question.

In this paper, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct…

The space of shapes of a polyhedron with given total angles less than 2\pi at each of its n vertices has a Kaehler metric, locally isometric to complex hyperbolic space CH^{n-3}. The metric is not complete: collisions between vertices take…

Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that…

Sectional curvature bounds are of central importance in the study of Riemannian manifolds, both in smooth differential geometry and in the generalized synthetic setting of Alexandrov spaces. Riemannian metrics along with metric spaces of…

This is a review article on some applications of generalised parabolic structures to the study of torsion free sheaves and $L$-twisted Hitchin pairs on nodal curves. In particular, we survey on the relation between representations of the…

We construct new complete, compact, inhomogeneous Einstein metrics on S^{m+2} sphere bundles over 2n-dimensional Einstein-Kahler spaces K_{2n}, for all n \ge 1 and all m \ge 1. We also obtain complete, compact, inhomogeneous Einstein…

Suppose that $\theta_1,\theta_2,\dots,\theta_n$ are positive numbers and $n\ge 3$. Does there exist a sphere with a spherical metric with $n$ conical singularities of angles $2\pi\theta_1,2\pi\theta_2,\dots,2\pi\theta_n$? A sufficient…

The so-called Hitchin-Kobayashi correspondence, proved by Donaldson, Uhlenbeck and Yau, establishes that an indecomposable holomorphic vector bundle over a compact Kahler manifold admits a Hermitian-Einstein metric if and only if the bundle…

We establish the correspondence between tame harmonic bundles and $\mu_L$-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for $\mu_L$-stable parabolic Higgs bundles.…

It is shown that a construction of Z. Zhang and Y. Xiao on open subsets of Ptolemaic spaces yields, when the subset has boundary containing at least two points, metrics that are Gromov hyperbolic with parameter $\log 2$ and strongly…

It is well known that a hyperbolic domain in the complex plane has uniformly perfect boundary precisely when the product of its hyperbolic density and the distance function to its boundary has a positive lower bound. We extend this…

We construct two-dimensional families of complex hyperbolic structures on disc orbibundles over the sphere with three cone points. This contrasts with the previously known examples of the same type, which are locally rigid. In particular,…

We study singular Hermitian metrics on vector bundles. There are two main results in this paper. The first one is on the coherence of the higher rank analogue of multiplier ideals for singular Hermitian metrics defined by global sections.…

In this paper we present a weighted $L_p$-theory of parabolic systems on a half space. The leading coefficients are assumed to be only measurable in $t$ and have small bounded mean oscillations (BMO) with respect to $x$, and the lower order…

Let $(X,\,D)$ be an $m$-pointed compact Riemann surface of genus at least $2$. For each $x \,\in\, D$, fix full flag and concentrated weight system $\alpha$. Let $P \mathcal{M}_{\xi}$ denote the moduli space of semi-stable parabolic vector…