Positive Mass Theorem for Manifolds with Fibered Euclidean Ends
Positive Mass Theorem for Manifolds with Fibered Euclidean Ends
-
Xianzhe Dai, University of California, Santa Barbara
The famous Positive Mass Theorem of Schoen-Yau and Witten states that an asymptotically Euclidean manifold with nonnegative scalar curvature must have nonnegative ADM mass (if the dimension of the manifold is between $3$ and $7$ or if the manifold is spin). Moreover, the mass is zero iff the manifold is the Euclidean space. Recently there has been a lot of interest and activity in听Positive Mass Theorems for spaces which are asymptotically approaching an Euclidean space times a compact manifold. We will discuss some of the work in this direction听going back to our earlier work as well as some of our recent work and related work by others.