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题目：Nonnegative Ricci curvature, nilpotency, and Hausdorff dimension

报告人：潘佳垠教授 (UC-Santa Cruz)

Abstract:

Collapsed Ricci limit spaces in general may admit isometric orbits whose Hausdorff dimension exceeds their topological dimension. The first examples with this feature are constructed by Pan-Wei as the asymptotic cone of the universal cover of an open (complete and non-compact) manifold M with Ric≥ 0 and π_1  (M)=Z. In the same paper, we asked whether the (non-abelian) nilpotency of π_1 (M) implies the existence of some asymptotic R-orbit of large Hausdorff dimension. In this talk, we give an affirmative answer. More precisely, given an open manifold M with Ric≥ 0 and escape rate not 1/2, we show that if π_1 (M) contains a torsion-free nilpotent subgroup of nilpotency step l, then there is an asymptotic cone (Y,y) of the universal cover and a closed R-subgroup L of the isometry group of Y such that the orbit Ly has Hausdorff dimension at least l. This also extends previously known results on virtual abelianness.

时间：2023-8-1始第一周，周二、周三、周五上午9:30-11:30；第二周，周二、周三、周四上午

地点：校本部教二楼613教室

邀请人：戎小春、胥世成    欢迎老师同学们参加！