Repulsion and quantization in almost-harmonic maps, and asymptotics of the harmonic map flow

• 成果类型: Article
• 署名作者: Topping, P
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.159.465
• 发表日期: 2004
• 页码: 465-534
• 关键词: surfaces; EVOLUTION; mappings

摘要

We present an analysis of bounded-energy low-tension maps between 2-spheres. By deriving sharp estimates for the ratio of length scales on which bubbles of opposite orientation develop, we show that we can establish a 'quantization estimate' which constrains the energy of the map to lie near to a discrete energy spectrum. One application is to the asymptotics of the harmonic map flow; we find uniform exponential convergence in time, in the case under consideration.