Related papers: Extremal Kaehler Metrics and Bach-Merkulov Equatio…

In this paper, we study rotationally symmetric extremal K\"ahler metrics on $\mathbb C^n$ ($n\geq 2$) and $\mathbb C^2 \backslash\{0\}$. We present a classification of such metrics based on the zeros of the polynomial appearing in Calabi's…

In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we…

In this paper, we study one typical Einstein-Weyl equation. It arises from Ferapontov and Kruglikov's investigation on the integrability of several dispersionless partial differential equations and the geometry of their formal…

We establish the convexity of Mabuchi's K-energy functional along weak geodesics in the space of Kahler potentials on a compact Kahler manifold thus confirming a conjecture of Chen and give some applications in Kahler geometry, including a…

Given a compact Kahler manifold with an extremal metric (M,\omega), we give sufficient conditions on finite sets points p_1,...,p_n and weights a_1,...a_n for which the blow up of M at p_1,...,p_n has an extremal metric in the Kahler class…

Let $M=G/K$ be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group $G$. We use the variational approach to find invariant Einstein metrics for all flag manifolds with two isotropy summands. We also…

A construction of Kaehler-Einstein metrics using Galois coverings, studied by Arezzo-Ghigi-Pirola, is generalized to orbifolds. By applying it to certain orbifold covers of P^n which are trivial set theoretically, one obtains new Einstein…

We first provide an alternative proof of the classical Weitzneb\"ock formula for Einstein four-manifolds using Berger curvature decomposition, motivated by which we establish a unified framework for a Weitzenb\"ock formula for a large class…

In this paper we study the set of balanced metrics (in Donaldson's terminology) on a compact complex manifold M which are homothetic to a given balanced one. This question is related to various properties of the Tian-Yau-Zelditch…

We study the construction and classification of weakly Bochner-flat (WBF) metrics (i.e., Kahler metrics with coclosed Bochner tensor) on compact complex manifolds. A Kahler metric is WBF if and only if its `normalized' Ricci form is a…

The Hitchin-Kobayashi correspondence for vector bundles, established by Donaldson, Kobayashi, Luebke, Uhlenbeck and Yau, states that an indecomposable holomorphic vector bundle over a compact Kaehler manifold is stable in the sense of…

Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock - Ivanenko. In…

H. Akbar-Zadeh has recently proposed (J Geom Phys 17 (1995) 342) a new geometric formulation of Einstein-Maxwell system with source in terms of what are called "Generalized Einstein manifolds". We show that, contrary to the claim, Maxwell…

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on…

This article is an expository introduction to our paper Convexity of the K-energy and Uniqueness of Extremal metrics. We present the main ideas behind the proof that Mabuchi's K-energy functional is convex along weak geodesics in the space…

We present and discuss a 4-parameter stationary axisymmetric solution of the Einstein-Maxwell equations able to describe the exterior field of a rotating magnetized deformed mass. The solution arises as a system of two overlapping…

Electromagnetic waves arise in many area of physics. Solutions are difficult to find in the general case. In this paper, we numerically integrate Maxwell equations in a 3D spherical polar coordinate system. Straightforward finite difference…

We consider non-Kaehler compact complex manifolds which are homogeneous under the action of a compact Lie group of biholomorphisms and we investigate the existence of special (invariant) Hermitian metrics on these spaces. We focus on a…

We study compactness for nonnegative solutions of the fourth order constant $Q$-curvature equations on smooth compact Riemannian manifolds of dimension $\ge 5$. If the $Q$-curvature equals $-1$, we prove that all solutions are universally…

Consider a compact K\"ahler manifold which either admits an extremal K\"ahler metric, or is a small deformation of such a manifold. We show that the blowup of the manifold at a point admits an extremal K\"ahler metric in K\"ahler classes…