报告摘要：An Alexandrov space is a metric space of curvature bounded below. A typical example of Alexandrov spaces is the Gromov-Hausdorff limit of Riemannian manifolds of sectional curvature bounded from below. Sometimes, Alexandrov spaces are useful to study the Gromov-Hausdorff convergence/collapsing phenomena under a lower bound of sectional curvature. In this lecture, I show the study of geometric analysis on Alexandrov space. We begin with the smooth differentiable structure and Riemannian metric on an Alexandrov space. Then we define the Dirichlet energy form and Laplacian. We show an Poincare inequality and the almost polarity of the singular set, both which are important to get some basic property for geometric analysis on Alexandrov spaces. The final goal is a splitting theorem under the infinitesimal version of volume comparison condition. This is a generalization of a famous splitting theorem due to Cheeger-Gromoll under nonnegative Ricci curvature. A key in the proof is a Laplacian comparison result.

报告时间：12月3日（星期三）、12月5日（星期五）下午 2:30-4:30

报告地点：光华东主楼1801室