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Mathematics Colloquium

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Date:  Tuesday, November 28, 2006

Title:  The Yamabe Problem: An Interaction between Geometry and Relativity

Abstract:  In this lecture we will discuss the geometric question of construction of Riemannian metrics of constant scalar curvature. This problem turns out to have an intimate connection with gravitational mass in relativity. We will discuss this connection and survey the recent activity on the Yamabe problem which has provided a much more thorough understanding of constant scalar curvature metrics both from a variational and heat equation point of view. We will discuss the compactness conjecture and its consequences for general (not necessarily minimizing) solutions of the Yamabe problem made by the speaker over 15 years ago. Through the work of several researchers this had been established in some cases (low dimensions, locally conformally flat), but the full conjecture has been open. We will describe recent work concerning the general case.


Speaker:  Rick Schoen
Institution:  Stanford

 

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