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The gradient flow of Higgs pairs

Jiayu Li, Xi Zhang (2011)

Journal of the European Mathematical Society

We consider the gradient flow of the Yang–Mills–Higgs functional of Higgs pairs on a Hermitian vector bundle $(E, H_{0})$ over a Kähler surface $(M, ω)$ , and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition $(A_{0}, φ_{0})$ converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point $(A_{\infty}, φ_{\infty})$ of this functional. We also prove that the limiting Higgs pair $(A_{\infty}, φ_{\infty})$ can be extended smoothly to a vector bundle $E_{\infty}$ over...

The $L^{2}$ metric in gauge theory: an introduction and some applications

David Groisser (1997)

Banach Center Publications

We discuss the geometry of the Yang-Mills configuration spaces and moduli spaces with respect to the $L^{2}$ metric. We also consider an application to a de Rham-theoretic version of Donaldson’s μ-map.

The relation between the associate almost complex structure to $H M^{'}$ and $(H M^{'}, S, T)$ -Cartan connections.

Esrafilian, Ebrahim, Salimi Moghaddam, Hamid Reza (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The Schouten-van Kampen Affine Connections Adapted to Almost (Para)Contact Metric Structures

Zbigniew Olszak (2013)

Publications de l'Institut Mathématique

The singularities of Yang-Mills connections for bundles on a surface.

Johannes Huebschmann (1996)

Mathematische Zeitschrift

The singularity structureοf the Yang-Mills configuration space

Jürgen Fuchs (1997)

Banach Center Publications

The geometric description of Yang–Mills theories and their configuration space $ℳ$ is reviewed. The presence of singularities in M is explained and some of their properties are described. The singularity structure is analysed in detail for structure group SU(2). This review is based on [28].

The structure of pseudo-holomorphic subvarieties for a degenerate almost complex structure and symplectic form on $S^{1} \times B^{3}$ .

Taubes, Clifford Henry (1998)

Geometry & Topology

Displaying 1 – 10 of 10

The gradient flow of Higgs pairs

The $L^{2}$ metric in gauge theory: an introduction and some applications

The relation between the associate almost complex structure to $H M^{'}$ and $(H M^{'}, S, T)$ -Cartan connections.

The Schouten-van Kampen Affine Connections Adapted to Almost (Para)Contact Metric Structures

The singularities of Yang-Mills connections for bundles on a surface.

The singularity structureοf the Yang-Mills configuration space

The structure of pseudo-holomorphic subvarieties for a degenerate almost complex structure and symplectic form on $S^{1} \times B^{3}$ .

The torsion of spinor connections and related structures.

Theory of the zero order effect suitable to investigate the space-time geometrical properties.

Torsion, curvature and deflection $d$ -tensors on $J^{1} (T, M)$ .

Currently displaying 1 – 10 of 10