Related papers: Balanced metrics on Hartogs domains

We introduce two notions of hyperbolicity for not necessarily K\"ahler $n$-dimensional compact complex manifolds $X$. The first, called {\it balanced hyperbolicity}, generalises Gromov's K\"ahler hyperbolicity by means of Gauduchon's…

Let $X$ be an arbitrary non-compact hyperbolic Riemann surface, that is, not $\mathbb C$ or $\mathbb C^*$. Given a tuple of holomorphic differentials $\boldsymbol q=(q_2,\cdots,q_n)$ on $X$, one can define a Higgs bundle…

A manifold (M,I,J,K) is called hypercomplex if I,J,K are complex structures satisfying quaternionic relations. A quaternionic Hermitian metric is called HKT (hyperkaehler with torsion) if $Id\omega_I = Jd \omega_J=Kd\omega_K$, where…

We present an analytical proof that certain natural metric planar universal covers are Hadamard metric spaces. In particular if $\rho=\varphi\circ u$ where $u$ is locally Lipschitz and subharmonic in $\Omega$, $\varphi$ is positive and…

Harmonic maps from S^2 to S^2 are all weakly conformal, and so are represented by rational maps. This paper presents a study of the L^2 metric gamma on M_n, the space of degree n harmonic maps S^2 -> S^2, or equivalently, the space of…

We classify the effective and transitive actions of a Lie group $G$ on an n-dimensional non-degenerate hyperboloid (also called real pseudo-hyperbolic space), under the assumption that $G$ is a closed, connected Lie subgroup of…

In this paper we investigate the moduli space of parabolic Higgs bundles over a punctured Riemann surface with varying weights at the punctures. We show that the harmonic metric depends analytically on the weights and the stable Higgs…

Consider a domain $\varOmega$ in $\mathbb{C}^n$ with $n\geqslant 2$ and a compact subset $K\subset\varOmega$ such that $\varOmega\backslash K$ is connected. We address the problem whether a holomorphic line bundle defined on…

The space of $G$-invariant metrics on a homogeneous space $G/H$ is in one-to-one correspondence with the set of inner products on the tangent space $\fr{m}\cong T_{{\it o}}(G/H)$, which are invariant under the isotropy representation. When…

We prove that a Hilbert domain which is quasi-isometric to a normed vector space is actually a convex polytope.

We propose the metric notion of strong hyperbolicity as a way of obtaining hyperbolicity with sharp additional properties. Specifically, strongly hyperbolic spaces are Gromov hyperbolic spaces that are metrically well-behaved at infinity,…

We show that certain space of vector valued harmonic weak Maass forms of half integral weight is isomorphic to a space of scalar valued ones whose Fourier coefficients are supported on suitable progressions. This kind of result for…

It was recently shown that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a domain with an $n-1$ dimensional uniformly rectifiable boundary, in the presence of now well understood additional…

A new metric on the open 2-dimensional unit disk is defined making it a geodesically complete metric space whose geodesic lines are precisely the Euclidean straight lines. Moreover, it is shown that the unit disk with this new metric is not…

We show that if a Fano manifold has discrete automorphism group and admits a polarized K\"ahler-Einstein metric, then there exists a sequence of anticanonically balanced metrics converging smoothly to the K\"ahler-Einstein metric. Our proof…

We show that the equality $m_1(f(x))=m_2(g(x))$ for $x$ in a neighborhood of a point $a$ remains valid for all $x$ provided that $f$ and $g$ are open holomorphic maps, $f(a)=g(a)=0$ and $m_1,$ $m_2$ are Minkowski functionals of bounded…

We show that, given a real or complex hyperbolic metric $g_0$ on a closed manifold $M$ of dimension $n\geq 3$, there exists a neighborhood $\mathcal U$ of $g_0$ in the space of negatively curved metrics such that for any $g\in \mathcal U$,…

The Fock-Bargmann-Hartogs domain $D_{n,m}$ in $\mathbb{C}^{n+m}$ is defined by the inequality $\|w\|^2<e^{-\|z\|^2},$ where $(z,w)\in \mathbb{C}^n\times \mathbb{C}^m$, which is an unbounded non-hyperbolic domain in $\mathbb{C}^{n+m}$. This…

The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…

We consider Non Autonomous Conformal Iterative Function Systems (NACIFS) and their limit set. Our main concern is harmonic measure and its dimensions : Hausdorff and Packing. We prove that this two dimensions are continuous under…