中科院数学与系统科学研究院
数学研究所
学术报告
非线性分析研讨班
报告人：Melanie Rupflin（Oxford）
题 目：Sharp quantitative rigidity results for maps between spheres of general degree
时 间：2023.11.02（星期四）17:00-18:00
地 点：Zoom: 679 0093 7038 Code: 827531
摘 要：As the energy of any map v of degree k>0 from S^2 to S^2 is at least 4\pi k with equality if and only if v is a rational map, it is natural to ask whether maps with small energy defect E(v)-4\pi k are necessarily close to a rational map. While such a rigidity statement turns out to be false for maps of general degree, we will explain in this talk that any map with small energy defect is essentially given by a collection of rational maps that describe the behaviour of the map at very different scales and that the distance of any map to such collections is controlled by a sharp quantitative rigidity estimate.
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