首页 > 数学科学研究所 > 师资队伍 > 蔡明亮个人简介
蔡明亮    副所长、正教授
所在学院 数学科学研究所
研究方向 微分几何,数学相对论
联系方式 caiml@@shanghaitech.edu.cn
 
  个人简介  
1978.10-1982.07,江苏师范大学(原徐州师范学院),本科
1982.09-1985.07,南京大学,硕士研究生
1985.09-1991.05,宾夕法尼亚大学,博士研究生
1991.08-1997.07,迈阿密大学,助理教授
1997.07–至今,迈阿密大学,副教授
2018.12–至今,上海科技大学,数学科学研究所常任正教授、副所长
  主要研究内容  
具有几乎非负Ricci 曲率的非紧流形的拓扑结构,具有非负数量曲率流形的几何结构,黑洞的拓扑结构,以及渐进平坦、渐进双曲流形的正质量和刚性问题。
  代表性论文  
1. Ends of Riemannian manifolds with nonnegative Ricci curvature outside a compact set.  Bull. Amer. Soc., 2 (1991), P. 371-377.
2. A splitting theorem for manifolds of almost nonnegative Ricci curvature.  Ann. Global Analysis and Geometry. 11 (1993), P. 373-385.
3. On Gromov's large Riemannian manifolds, Geometriae Dedicata. 50 (1994), P. 37-45.
4. (With Tobias Colding and DaGang Yang) A gap theorem for ends of open Riemannian manifolds.  Proc. Amer. Math. Soci. (123) 1995. P.247-250.
5. (with G. Galloway) Rigidity of tori in 3-manifolds of non-negative Scalar Curvature.  Comm. Anal. Geom. 8(2000), p. 565-573.
6. (with G. Galloway) Boundaries of zero scalar curvature in the Ads/CFT correspondence.  Adv. Theor. Math. Phys. 3 (2000), no. 6, 1769-1783.
7. (with G. Galloway) On the topology and area of black holes.  Classical Quantum Gravity 18 (2001), no. 14, 2707-2718.
8. Volume Minimizing hypersurfaces in Manifolds of nonnegative scalar curvature. Advnced Studies in Pure Mathematics 34, 2002.  Minimal surfaces, Geometric Analysis and Simplectic Geometric. P. 1-7.
9. (with Lars Anderson and Greg Galloway) Rigidity and positivity of mass for asymptotic hyperbolic manifolds. Ann. Henri Poncare, 9(2008) 1-33.
10. On rigidity of gradient shrinking Ricci soliton of nonnegative sectional curvature. Pacific Journal of Mathematics, 271(2015), 61-76
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