The Yang-Mills flow in four dimensions
From MaRDI portal
Publication:1327490
DOI10.1007/BF01191339zbMath0807.58010MaRDI QIDQ1327490
Publication date: 28 February 1995
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) Initial value problems for linear higher-order PDEs (35G10) Connections (general theory) (53C05) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15) Higher-order parabolic equations (35K25)
Related Items
Stability and energy identity for Yang–Mills–Higgs pairs ⋮ GRADIENT FLOWS OF HIGHER ORDER YANG–MILLS–HIGGS FUNCTIONALS ⋮ On the blow-up set of the Yang-Mills flow on Kähler surfaces ⋮ Geometric evolution equations in critical dimensions ⋮ A Concentration-Collapse Decomposition forL2Flow Singularities ⋮ Instantons and singularities in the Yang-Mills flow ⋮ A conformally invariant gap theorem in Yang-Mills theory ⋮ Singularity formation of the Yang-Mills flow ⋮ The energy identity for a sequence of Yang-Mills \(\alpha \)-connections ⋮ Higher order Yang-Mills flow ⋮ ON THE STUDY OF ONE FLOW FOR ASD CONNECTION ⋮ The Yang-Mills flow for cylindrical end 4-manifolds ⋮ A probabilistic approach to the Yang-Mills heat equation. ⋮ Conformal bach flow ⋮ Morse homology for the Yang-Mills gradient flow ⋮ Yang-Mills replacement ⋮ Yang-Mills flow on special-holonomy manifolds ⋮ The threshold theorem for the $(4+1)$-dimensional Yang–Mills equation: An overview of the proof ⋮ Local regularity for the harmonic map and Yang-Mills heat flows ⋮ The coupled Yang-Mills-Higgs flow ⋮ Anti-self-dual connections and their related flow on 4-manifolds ⋮ Heat flow of Yang-Mills-Higgs functionals in dimension two ⋮ The Li-Yau-Hamilton estimate and the Yang-Mills heat equation on manifolds with boundary ⋮ Asymptotical behaviour of the Yang-Mills flow and singular Yang-Mills connections ⋮ Biharmonic map heat flow into manifolds of nonpositive curvature ⋮ The extrinsic polyharmonic map heat flow in the critical dimension ⋮ The gradient flow for gauged harmonic map in dimension two. II ⋮ Long-time existence for Yang-Mills flow ⋮ A Yang-Mills-Higgs gradient flow on \(\mathbb{R}^3\) blowing up at infinity ⋮ Collapsing in theL2Curvature Flow ⋮ Higher order Seiberg-Witten functionals and their associated gradient flows ⋮ Removable singularities of weak solutions to the navier-stokes equations ⋮ Stabilities of homothetically shrinking Yang-Mills solitons ⋮ Elliptic Yang–Mills flow theory ⋮ Nonuniqueness for the Yang--Mills heat flow. ⋮ Finite energy global well-posedness of the Yang-Mills equations on \(\mathbb{R}^{1+3}\): an approach using the Yang-Mills heat flow
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the evolution of harmonic mappings of Riemannian surfaces
- On the evolution of harmonic maps in higher dimensions
- Compactness of the moduli space of Yang-Mills connections in higher dimensions
- Stability and isolation phenomena for Yang-Mills fields
- Connections with \(L^ p \)bounds on curvature
- The approximation problem for Sobolev maps between two manifolds
- Monotonicity formulas for parabolic flows on manifolds
- Monotonicity formula and small action regularity for Yang-Mills flows in higher dimensions
- Finite time blowing-up for the Yang-Mills gradient flow in higher dimensions
- A direct method for minimizing the Yang-Mills functional over 4- manifolds
- The Yang-Mills equations over Riemann surfaces
- Removable singularities in Yang-Mills fields