Bubbling of almost-harmonic maps between 2-spheres at points of zero energy density
UNSPECIFIED (2004) Bubbling of almost-harmonic maps between 2-spheres at points of zero energy density. In: Conference on Harmonic Maps, Minimal Surfaces and Geometric Flows, Univ Bretagne Occidentale, Brest, FRANCE, JUL 07-12, 2002. Published in: VARIATIONAL PROBLEMS IN RIEMANNIAN GEOMETRY: BUBBLES, SCANS AND GEOMETRIC FLOWS, 59 pp. 33-42.Full text not available from this repository.
We show that bubbling of almost-harmonic maps between 2-spheres has very different behaviour depending on whether or not bubbles develop at points in the domain at which the energy density of the body map is zero. We also see that this translates into different behaviour for the harmonic map flow. In  we obtained results, assuming nonzero bubble point density for certain bubbles, forcing the harmonic map flow to converge uniformly and exponentially to its limit. This involved proving a type of nondegeneracy for the harmonic map energy (a 'quantization' estimate') and an estimate on certain bubble scales (a repulsion' estimate). Here we show that without the nonzero bubble point density hypothesis, both the quantization and repulsion estimates fail, and we construct a flow in which the convergence is no longer exponentially fast.
|Item Type:||Conference Item (UNSPECIFIED)|
|Subjects:||Q Science > QA Mathematics|
|Series Name:||PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS|
|Journal or Publication Title:||VARIATIONAL PROBLEMS IN RIEMANNIAN GEOMETRY: BUBBLES, SCANS AND GEOMETRIC FLOWS|
|Publisher:||BIRKHAUSER VERLAG AG|
|Editor:||Baird, P and ElSoufi, A and Fardoun, A and Regbaoui, R|
|Number of Pages:||10|
|Page Range:||pp. 33-42|
|Title of Event:||Conference on Harmonic Maps, Minimal Surfaces and Geometric Flows|
|Location of Event:||Univ Bretagne Occidentale, Brest, FRANCE|
|Date(s) of Event:||JUL 07-12, 2002|
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