Related papers: Direct Images and Hilbert Fields

Let X be a compact Riemann surface equipped with a real-analytic K\"ahler form $\omega$ and let E be a holomorphic vector bundle over $X$ equipped with a real-analytic Hermitian metric $h$. Suppose that the curvature of $h$ is…

We look at smooth manifolds equipped with a possibly singular Riemannian metric. We give sufficient conditions for the existence of scalar curvature measures and Dirac operators.

This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the…

Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…

In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the…

We establish a compact analog of the P = W conjecture. For a holomorphic symplectic variety with a Lagrangian fibration, we show that the perverse numbers associated with the fibration match perfectly with the Hodge numbers of the total…

We prove that the existence of a Hurewicz fibration between certain spaces with the homotopy type of a CW-complex implies some topological restrictions on their universal coverings. This result is used to deduce differentiable and metric…

In this paper we consider the following question: For bounded domains with smooth boundary, can strong pseudoconvexity be characterized in terms of the intrinsic complex geometry of the domain? Our approach to answering this question is…

We study on the biholomorphic equivalence of a strongly pseudoconvex bounded domain with differentiable spherical boundary to an open ball, and we study on the biholomorphicity of a proper holomorphic self mapping of a strongly pseudoconvex…

We give a mathematical exposition of the Page metric, and introduce an efficient coordinate system for it. We carefully examine the submanifolds of the underlying smooth manifold, and show that the Page metric does not have positive…

Let $p:\sXS$ be a proper K\"ahler fibration and $\sE\sX$ a Hermitian holomorphic vector bundle. As motivated by the work of Berndtsson(\cite{Berndtsson09a}), by using basic Hodge theory, we derive several general curvature formulas for the…

This paper is a sequel to \cite{Berndtsson}. In that paper we studied the vector bundle associated to the direct image of the relative canonical bundle of a smooth K\"ahler morphism, twisted with a semipositive line bundle. We proved that…

Let B be the Bergman projection associated to a domain on which the dbar-Neumann operator is compact. We show that arbitrary L^2 derivatives of Bf are controlled by derivatives of f taken in a single, distinguished direction. As a…

We review some basic concepts related to convex real projective structures from the differential geometry point of view. We start by recalling a Riemannian metric which originates in the study of affine spheres using the Blaschke connection…

We present some results dealing with the local geometry of almost complex manifolds. We establish mainly the complete hyperbolicity of strictly pseudoconvex domains, the extension of plurisubharmonic functions through generic submanifolds…

The space of differential operators acting on skewsymmetric tensor fields or on smooth forms of a smooth manifold are representations of its Lie algebra of vector fields. We compute the first cohomology spaces of these representations and…

In this article we are interested in the differential geometric properties of certain higher direct images of exterior powers of the sheaf of relative differentials twisted with a line bundle. We obtain explicit curvature formulas,…

We first want to consider the formal deformation of a fibered manifold $P \rightarrow M$ as a (bi-)module or subalgebra, where $M$ has a given differential star product. Consequently we want to find obstructions for the existence of a…

In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to…

We study holomorphic symplectic manifolds which are fibred by abelian varieties. This structure is a higher dimensional analogue of an elliptic fibration on a K3 surface. We investigate when a holomorphic symplectic manifold is fibred in…