Related papers: Explicit Hodge decomposition on Riemann surfaces
We construct an explicit homotopy formula for the d-bar complex on a complete intersection subvariety V in CP^n. This formula can be interpreted as a Hodge-type decomposition for residual currents on V.
We construct explicit equations of Cartwright-Steger and related surfaces.
We have obtained the explicit versions and precisions for the Hodge-Riemann decomposition of formes on affine algebraic curve V. The main application consists in the construction of Faddeev-Green function for Laplacian on V. Basing on this…
A leafwise Hodge decomposition was proved by Sanguiao for Riemannian foliations of bounded geometry. Its proof is explained again in terms of our study of bounded geometry for Riemannian foliations. It is used to associate smoothing…
The Hodge-de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study…
The Hodge decomposition is well-known for compact manifolds. The result has been extended by Kodaira to include non-compact manifolds and $L^2$ forms. We further extend the Hodge decomposition to the Sobolev space $H^1$ for general…
We give an abstract version of the hard Lefschetz theorem, the Lefschetz decomposition and the Hodge-Riemann theorem for compact Kaehler manifolds.
We prove a version of the $L^p$ hodge decomposition for differential forms in Euclidean space and a generalization to the class of Lizorkin currents. We also compute the $L_{qp}-$cohomology of $\mathbb{R}^n$.
We provide an explicit algebraic construction for the pullback and direct image of parabolic bundles, parabolic Higgs bundles and parabolic connections through maps between Riemann surfaces. We show that these constructions preserve…
We construct an explicit, multiplicative Chow-K\"unneth decomposition for the Hilbert scheme of points of a K3 surface. We further refine this decomposition with respect to the action of the Looijenga-Lunts-Verbitsky Lie algebra.
We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module…
The purpose of this article is to give another molecular decomposition for members of the weighted Hardy spaces.
The Hodge decomposition is a fundamental result in differential geometry and algebraic topology, particularly in the study of differential forms on a Riemannian manifold. Despite extensive research in the past few decades,…
An outline of the basic Riemannian structures underlying the separation of variables in the Hamilton-Jacobi equation of natural Hamiltonian systems.
On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.
Let $X$ denote a compact set which is laminated by Riemann surfaces. We assume that $X$ carries a positive CR line bundle $ L\rightarrow X$. The main result of the paper is that there exists a positive integer $s$ so that if $v$ is any…
We prove that a standard realization of the direct image complex via the so-called Douady-Barlet morphism associated with a smooth complex analytic surface admits a natural decomposition in the form of an injective quasi-isomorphism of…
On a compact $\partial\bar\partial$-manifold $X$, one has the Hodge decomposition: the de Rham cohomology groups split into subspaces of pure-type classes as $H_{dR}^k (X)=\oplus_{p+q=k}H^{p,\,q}(X)$, where the $H^{p,\,q}(X)$ are…
By modifying Cole's example, we construct explicit Riemann surfaces with large bounds on corona solutions in an elementary way.
The Hamilton-Jacobi equation for a Hamiltonian section on a Lie affgebroid is introduced and some examples are discussed.