演講者：陳文豪教授

單　位：東海大學數學系

日　期：2010年3月31日　PM 14:30

地　點：國立高雄大學理學院408室

講　題：Rigidity of Manifolds under Lower Curvature Bounds 

摘　要：

Rigidity is one of the most interesting properties in geometry. For example, there are infinitely many regular n-polygons in a 2-dimensional plane but only five Plato regular solids in 3-dimensional space. In Riemannian geometry, rigidity results from investigating the relationships between curvature and topology of a Riemannian manifold. It is known that Gauss-Bonnet theorem characterizes closed 2-manifolds with positive, zero or negative curvature. For a compact hyperbolic manifold with dimension at least 3, Mostow’s rigidity theorem reveals that the algebraic structure determines the geometric structure. Myers’ theorem shows the finiteness of the fundamental group and an estimation of the diameter for a compact Riemannian manifold with positive Ricci curvature. In this talk, we will present partial extensions of these theorems via the notion of Gromov-Hausdorff distance. In addition, a combinatorial analogue of Ricci curvature and a rigidity of combinatorial manifolds will be also mentioned.