Related papers: On Homothetic Balanced Metrics

In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by Higgs fields, and call Donaldson-Thomas equation, to analytically approach the…

We study Kahler surfaces with harmonic anti-selfdual Weyl tensor. We provide an explicit local description, which we use to obtain the complete classification in the compact case. We give new examples of extremal Kahler metrics, including…

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of…

The metrics of S. Y. Cheng and S.-T. Yau are considered on a strictly pseudoconvex domains in a complex manifold. Such a manifold carries a complete K\"{a}hler-Einstein metric if and only if its canonical bundle is positive. We consider the…

We prove the existence of non-positively curved K\"ahler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact K\"ahler manifold, under a technical condition on the cone angles, and we also…

Oeljeklaus-Toma (OT) manifolds are higher dimensional analogues of Inoue-Bombieri surfaces and their construction is associated to a finite extension $K$ of $Q$ and a subgroup of units $U$. We characterize the existence of pluriclosed…

Given a flat metric one may generate a local Hamiltonian structure via the fundamental result of Dubrovin and Novikov. More generally, a flat pencil of metrics will generate a local bi-Hamiltonian structure, and with additional…

Given a metric defined on a manifold of dimension three, we study the problem of finding a conformal filling by a Poincar\'e-Einstein metric on a manifold of dimension four. We establish a compactness result for classes of conformally…

We continue our study on Hermitian manifolds that are {\em Bismut torsion parallel,} or {\em BTP} for brevity, which means that the Bismut connection has parallel torsion tensor. For $n\geq 3$, BTP metrics can be balanced (and…

The goal of this article is to study compact quasi-Einstein manifolds with boundary. We provide boundary estimates for compact quasi-Einstein manifolds simi\-lar to previous results obtained for static and $V$-static spaces. In addition, we…

We prove several vanishing theorems for the cohomology of balanced hyperbolic manifolds that we introduced in our previous work and for the $L^2$ harmonic spaces on the universal cover of these manifolds. Other results include a Hard…

Let $(X,L_{X})$ be an $n$-dimensional polarized manifold. Let $D$ be a smooth hypersurface defined by a holomorphic section of $L_{X}$. In this paper, we study the existence of a complete scalar-flat K\"{a}hler metric on $X \setminus D$ on…

In this work, we describe the asymptotic behavior of complete metrics with prescribed Ricci curvature on open Kahler manifolds that can be compactified by the addition of a smooth and ample divisor. First, we construct a explicit sequence…

Small deformations of the complex structure do not always preserve special metric properties in the Hermitian non-K\"ahler setting. In this paper, we find necessary conditions for the existence of smooth curves of balanced metrics…

Inspired by a parabolic system of Li-Yuan-Zhang and the continuity equation of La Nave-Tian, we study a system of elliptic equations for a K\"ahler metric $\omega$ and a closed $(1, 1)$-form $\alpha$. Assuming a uniform estimate for…

Building on the first two authors' previous results, we prove a general criterion for convergence of (possibly singular) Bergman measures towards equilibrium measures on complex manifolds. The criterion may be formulated in terms of growth…

We prove the equivariant holomorphic Morse inequalities for a holomorphic torus action on a holomorphic vector bundle over a compact Kahler manifold when the fixed-point set is not necessarily discrete. Such inequalities bound the twisted…

The standard (Berezin-Toeplitz) geometric quantization of a compact Kaehler manifold is restricted by integrality conditions. These restrictions can be circumvented by passing to the universal covering space, provided that the lift of the…

In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable…

If $M$ is the underlying smooth oriented $4$-manifold of a Del Pezzo surface, we consider the set of Riemannian metrics $h$ on $M$ such that $W^+(\omega , \omega )> 0$, where $W^+$ is the self-dual Weyl curvature of $h$, and $\omega$ is a…