Title: A short proof of Allard’s and Brakke’… 继续阅读A short proof of Allard’s and Brakke’s regularity theorems
标签： blowup
Curvature-Torsion Entropy for Twisted Curves under Curve Shortening Flow
Title: Curvature-Torsion Entropy for Twisted Curves und… 继续阅读Curvature-Torsion Entropy for Twisted Curves under Curve Shortening Flow
Bubbling analysis of a conformal heat flow for harmonic maps
Woongbae Park
We study a conformal heat flow for harmonic maps. It is known that global weak solution of the flow exists and smooth except at mostly finitely many singular points. In this paper, we conduct a bubbling analysis for a finite time singularity.
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 the family of multi-bubble configurations in continuous time.
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 one- instanton while developing a SD one-instanton as a bubble. The proof involves the expansion of connection forms with respect to some Coulomb gauge on long cylinders.