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： MUSTREAD
The geometry of $\Phi_{(3)}$-harmonic maps
Title: The geometry of $\Phi_{(3)}$-harmonic maps Autho… 继续阅读The geometry of $\Phi_{(3)}$-harmonic maps
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 of finite-energy critical points in Sobolev norms. Moreover,
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.