Related papers: The $\partial$-Operator and Real Holomorphic Vecto…
We study equivalence of invariant metrics on noncompact K\"ahler manifolds with a complete Bergman metric of bounded curvature. Especially only the boundedness of the ratio between Bergman kernel and the $n$-times wedge product of Bergman…
A non-hermitian deformation of the one-dimensional transverse Ising model is shown to have the property of quasi-hermiticity. The transverse Ising chain is obtained from the starting non-hermitian Hamiltonian through a similarity…
The subject of this paper is the explicit momentum construction of complete Einstein metrics by ODE methods. Using the Calabi ansatz, further generalized by Hwang-Singer, we show that there are non-trivial complete conformally K\"ahler…
This article describes some complex-analytic aspects of the moduli space of the finite-dimensional complex representations of a finite quiver, which are stable with respect to a fixed rational weight. We construct a natural structure of a…
The main result of this note essentially is that if the base and fibers of a compact fibration carry Hermitian metrics of positive holomorphic sectional curvature, then so does the total space of the fibration. The proof is based on the use…
In this paper, we study weighted composition operators on Bergman spaces of analytic functions which are square integrable on polydisk. We develop the study in full generality, meaning that the corresponding weighted composition operators…
Let $M$ be a holomorphic symplectic K\"ahler manifold equipped with a Lagrangian fibration $\pi$ with compact fibers. The base of this manifold is equipped with a special K\"ahler structure, that is, a K\"ahler structure $(I, g, \omega)$…
We propose and investigate two types, the latter with two variants, of notions of partial hyperbolicity accounting for several classes of compact complex manifolds behaving hyperbolically in certain directions, defined by a vector subbundle…
Let X be a strictly pseudoconcave domain in a closed polarized complex manifold (Y,L) where L is a (semi-)positive line bundle over Y. Any given Hermitian metric on L, together with a volume form, induces by restriction to X a Hilbert space…
We explore algebraic and spectral properties of weighted graphs containing twin vertices that are useful in quantum state transfer. We extend the notion of adjacency strong cospectrality to arbitrary Hermitian matrices, with focus on the…
We study asymptotic estimates of the dimension of cohomology on possibly non-compact complex manifolds for line bundles endowed with Hermitian metrics with algebraic singularities. We give a unified approach to establishing singular…
We discuss a technique to construct Ricci-flat hermitian metrics on complements of (some) anticanonical divisors of almost homogeneous manifolds and discuss when this metric is complete and K\"ahler. This construction has a strong interplay…
We explore complex Riemannian geometry and Hermitian metrics on complex algebraic varieties and analytic spaces, respectively. In particular, we introduce Hermitian metrics on holomorphic Lie algebroids and examine the associated…
Let $\psi$ be a holomorphic function on the open unit ball $\BB \subset \C^N$, and let $\varphi$ be a holomorphic self-map of $\BB$, associated with normal weights $\nu$ and $\mu$. We consider the weighted composition operator $…
We characterize the set of semiclassical measures corresponding to sequences of eigenfunctions of the attractive Coulomb operator $\widehat{H}_{\hbar}:=-\frac{\hbar^2}{2}\Delta_{\mathbb{R}^3}-\frac{1}{|x|}$. In particular, any Radon…
Criterions for constancy of the holomorphic sectional curvature and the antiholomorphic sectional curvature are proved for almost Hermitian manifolds. It is shown, that an almost Hermitian manifold satisfying the axiom of antiholomorphic…
In this paper we study numerical properties of quotients of holomorphic log-tensors.
We show for a certain class of operators $A$ and holomorphic functions $f$ that the functional calculus $A\mapsto f(A)$ is holomorphic. Using this result we are able to prove that fractional Laplacians $(1+\Delta^g)^p$ depend real…
An explicit surjection from a set of (locally defined) unconstrained holomorphic functions on a certain submanifold of (Sp_1(C) \times C^{4n}) onto the set HK_{p,q} of local isometry classes of real analytic pseudo-hyperk\"ahler metrics of…
We propose an approach to the existence problem for locally conformally K\"ahler metrics on compact complex manifolds by introducing and studying a functional that is different according to whether the complex dimension of the manifold is…