ArXiv – Page 4 – MathRlife

Van Abel May 10, 2023StatusArXivAbelian Yang-Mills-Higgs, asymptotic behaviour, compactness, monotonicity formula, MUSTREAD, rectifiable varifold Leave a comment

The Yang Mills Higgs functional on complex line…

The Yang-Mills-Higgs functional on complex line bundles: asymptotics for critical points Giacomo Canevari, Federico Luigi Dipasquale, Giandomenico Orlandi We consider a gauge-invariant Ginzburg-Landau functional (also known as Abelian Yang-Mills-Higgs model) on Hermitian line bundles over closed Riemannian manifolds of dimension n≥3. Assuming a logarithmic energy bound in the coupling parameter, we study the asymptotic behaviour of critical points in the non-self dual scaling, as the coupling parameter tends to zero. After a convenient choice of the gauge, we show compactness … Continue reading “The Yang Mills Higgs functional on complex line…”

Van Abel May 10, 2023StatusArXivany time sequence, blowup, continuous in time, harmonic maps, MUSTREAD Leave a comment

Continuous in time bubble decomposition for the harmonic…

Continuous in time bubble decomposition for the harmonic map heat flow Jacek Jendrej, Andrew Lawrie, Wilhelm Schlag We consider the harmonic map heat flow for maps from the plane to the two-sphere. It is known that solutions to the initial value problem exhibit bubbling along a well-chosen sequence of times. We prove that every sequence of times admits a subsequence along which bubbling occurs. This is deduced as a corollary of our main theorem, which shows that the solution approaches … Continue reading “Continuous in time bubble decomposition for the harmonic…”

Van Abel May 10, 2023StatusArXivchern classes, minimizing, Taubes construction, Yang-Mills Leave a comment

DIRECT MINIMIZING METHOD FOR YANG-MILLS ENERGY OVER SO(3) BUNDLE

DIRECT MINIMIZING METHOD FOR YANG-MILLS ENERGY OVER SO(3) BUNDLE In this paper, we use the direct minimizing method to find Yang- Mills connections for SO(3) bundles over closed four manifolds. By constructing test connections, we prove that a minimizing sequence converges strongly to a minimizer under certain assumptions. In case the strong convergence fails, we find an anti-selfdual (or selfdual) connection.

Van Abel May 10, 2023StatusArXivblowup, expansion of connection forms, Yang-Mills Leave a comment

ON THE BLOW-UP OF YANG-MILLS FIELDS IN DIMENSION FOUR

ON THE BLOW-UP OF YANG-MILLS FIELDS IN DIMENSION FOUR In this paper, we study the blow-up of a sequence of Yang-Mills connection with bounded energy on a four manifold. We prove a set of equations relating the geometry of the bubble connection at the infinity with the geometry of the limit connection at the energy concentration point. These equations exclude certain scenarios from happening, for example, there is no sequence of Yang-Mills SU(2) connections on S4 converging to an ASD … Continue reading “ON THE BLOW-UP OF YANG-MILLS FIELDS IN DIMENSION FOUR”

Van Abel May 9, 2023StatusArXivconjecture of R. Hamilton, Inverse mean curvature flow, Ricci flow Leave a comment

Inverse mean curvature flow and Ricci-pinched three-manifolds

Inverse mean curvature flow and Ricci-pinched three-manifolds Gerhard Huisken, Thomas Koerber Let (M,g) be a complete, connected, non-compact Riemannian three-manifold with non-negative Ricci curvature satisfying Ric≥εtr(Ric)g for some ε>0. In this note, we give a new proof based on inverse mean curvature flow that (M,g) is either flat or has non-Euclidean volume growth. In conjunction with results of J. Lott and of M.-C. Lee and P. Topping, this gives an alternative proof of a conjecture of R. Hamilton recently proven … Continue reading “Inverse mean curvature flow and Ricci-pinched three-manifolds”