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学术报告:The asymptotic behavior of the dimension of spaces of harmonic functions with polynomial growth

发布时间:2018年10月22日 浏览次数:发布者:mathky

报告人:黄显涛副教授

        中山大学

报告题目:The asymptotic behavior of the dimension of spaces of harmonic functions with polynomial growth

报告时间:2018年10月27日上午09:00

报告地点:海韵实验楼105

报告摘要:Suppose (M, g) is a noncompact Riemannian manifold with nonnegative Ricci curvature, and let hd(M) be the dimension of the space of harmonic functions with polynomial growth of growth order at most d. Colding and Minicozzi proved that hd(M) is finite. Later on, there are many researches which give better estimates of hd(M). In this talk, we will present the work on asymptotic behavior of hd(M) when d is large. More precisely, suppose that (M, g) has maximal volume growth and its tangent cone at infinity is unique, then when d is sufficiently large, we obtain some estimates of hd(M) in terms of the growth order d, the dimension n and the asymptotic volume ratio of (M, g)..

报告人简介:黄显涛博士毕业于中山大学,曾于清华大学丘成桐数学中心做博士后研究,现为中山大学副研究员。他研究的领域为几何分析,主要感兴趣的是几何流的应用,以及流形的曲率和几何拓扑相关问题,有多篇文章发表在 Comm. Anal. Geom,Math. Ann.等著名期刊上。

联系人:宋翀副教授

 

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