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学术报告:Coplanar CMC surfaces, complex projective structures, and polynomial quadratic differentials

发布时间:2018年01月12日 浏览次数:发布者:mathky

报告人:Robert Kusner教授

        University of Massachusetts at Amherst

题目:Coplanar CMC surfaces, complex projective structures, and polynomial quadratic differentials

时间:2018年01月12日下午16:30

地点:海韵实验楼105

报告摘要:Complete embedded constant mean curvature (CMC) surfaces of fixed, finite topology form a finite-dimensional moduli space. This moduli space is a real-analytic variety parametrized by the asymptotic data of the surfaces, and possibly by some square-integrable Jacobi fields. For coplanar CMC surfaces of genus 0 with k ends, such Jacobi fields must vanish, and this moduli space can be explicitly described: it is diffeomorphic to the space of k-point spherical metrics; these can be described, in turn, by holomorphic immersions from the plane to the 2-sphere whose Schwarzian is a polynomial with degree depending on k. The CMC surfaces corresponding to the polynomials 0 and 1 are, respectively, the round sphere and the 1-parameter family of unduloids, while those which correspond to the polynomial z are the 3-parameter family of triunduloids. Byviewing the Schwarzian as a quadratic differential and its real foliations, a compelling picture of this correspondence emerges. (If time permits, a new construction of coplanar CMC surfaces with genus 1, all of whose ends are cylindrical, will also be described.)

报告人简介:Robert Kunser 1988年加州大学伯克利分校数学博士,现任美国麻省大学Amherst分校教授,并担任著名的几何,分析,数值计算,图形学的研究中心(GANG)的主任。长期从事极小曲面和常平均曲率曲面的研究。

联系人:关波教授

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