Program
The Geometry of the Scalar Curvature
Student No.:50
Time:Thu 13:00-14:50, 2014-03-13 ~ 2014-06-12 (except for public holiday on May 1)
Instructor:Vlad Moraru  [MSC, Tsinghua University]
Place:Conference Room 1, Floor 1, jin Chun Yuan West Building
Starting Date:2014-3-13
Ending Date:2014-6-12

 

 

Description:

 

The course will examine several aspects of the role of the scalar curvature in Riemannian geometry and general relativity. After a brief review of some basic concepts in Riemannian geometry, we will discuss topological obstructions to positive scalar curvature metrics, and the relationship between stable minimal surfaces and the sign of the scalar curvature of the ambient 3-manifold. This will allow us to discuss the Schoen-Yau proof of the Positive Mass conjecture in general relativity. Later in the course we will discuss Bray's proof of the Riemannian Penrose inequality.

 

 

Prerequisite:

 

An introductory course in Riemannian geometry.

 

 

 

Reference: 

 

Bray, "The Penrose inequality in general relativity and volume comparison theorems involving scalar curvature," thesis, Stanford University (1997)

 

 

Schoen, “Variational theory for the total scalar curvature functional for Riemannian metrics and related topics”, Springer Lecture Notes in Mathematics Volume 1365, 1989, pp 120-154

 

Schoen, Yau, “On the structure of manifolds with positive scalar curvature”, Manuscripta Math. 28, 159-183 (1979)

 

Schoen, Yau, “On the proof of the positive mass conjecture in general relativity”, Commun. Math. Phys. 65 45-76 (1979)