• Corpus ID: 204950534

Weak Holomorphic Structures over Kähler Surfaces

  title={Weak Holomorphic Structures over K{\"a}hler Surfaces},
  author={Alexandru Păunoiu and Tristan Rivi{\'e}re},
  journal={arXiv: Differential Geometry},
In this work we prove that any unitary Sobolev $W^{1,2}$ connection of an Hermitian bundle over a 2-dimensional Kahler manifold whose curvature is $(1,1)$ defines a smooth holomorphic structure. We prove moreover that such a connection can be strongly approximated in any $W^{1,p}$ ($p<2$) norm by smooth connections satisfying the same integrability condition. 



Topological and analytical properties of Sobolev bundles, I: The critical case

We study the interrelationship between topological and analytical properties of Sobolev bundles and describe some of their applications to variational problems on principal bundles. We in particular

Geometry of four-manifolds

1. Four-manifolds 2. Connections 3. The Fourier transform and ADHM construction 4. Yang-Mills moduli spaces 5. Topology and connections 6. Stable holomorphic bundles over Kahler surfaces 7. Excision

Removable singularities in Yang-Mills fields

We show that a field satisfying the Yang-Mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite. We obtain the result that every

Differential Topology and Quantum Field Theory

A Topological Preliminary. Elliptic Operators. Cohomology of Sheaves and Bundles. Index Theory for Elliptic Operators. Some Algebraic Geometry. Infinite Dimensional Groups. Morse Theory. Instantons

The Space of Weak Connections in High Dimensions

The space of Sobolev connections, as it has been introduced for studying the variation of Yang-Mills Lagrangian in the critical dimension $4$, happens not to be weakly sequentially complete in

The resolution of the Yang-Mills Plateau problem in super-critical dimensions

Gauge theory and calibrated geometry, I

The geometry of submanifolds is intimately related to the theory of functions and vector bundles. It has been of fundamental importance to find out how those two objects interact in many geometric

Multiple Integrals in the Calculus of Variations

Semi-classical results.- The spaces Hmp and Hmp0.- Existence theorems.- Differentiability of weak solutions.- Regularity theorems for the solutions of general elliptic systems and boundary value

The Neumann problem for the Cauchy-Riemann complex

Part explanation of important recent work, and part introduction to some of the techniques of modern partial differential equations, this monograph is a self-contained exposition of the Neumann

Principles of Algebraic Geometry

A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications