中科院数学与系统科学研究院

数学研究所

微分几何研讨班

报告人： 黄显涛 (中山大学)

题  目：The asymptotic behavior of the dimension of spaces of harmonic functions with polynomial growth

时  间：2018.11.30（星期五）, 16:00-17:00

地  点：数学院南楼N913室

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).