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, JUL 07-12, 2002, Univ Bretagne Occidentale, Brest, FRANCE.

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Abstract

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 [11] 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
ISBN:	3-7643-2432-5
Editor:	Baird, P and ElSoufi, A and Fardoun, A and Regbaoui, R
Date:	2004
Volume:	59
Number of Pages:	10
Page Range:	pp. 33-42
Publication Status:	Published
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
URI:	http://wrap.warwick.ac.uk/id/eprint/7652

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