Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606125 | Differential Geometry and its Applications | 2014 | 16 Pages |
Abstract
In this paper, we prove the almost Schur theorem, introduced by De Lellis and Topping, for the Riemannian manifold M of nonnegative Ricci curvature with totally geodesic boundary. Examples are given to show that it is optimal when the dimension of M is at least 5. We also prove that the almost Schur theorem is true when M is a 4-dimensional manifold of nonnegative scalar curvature with totally geodesic boundary. Finally we obtain a generalization of the almost Schur theorem in all dimensions only by assuming the Ricci curvature is bounded below.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Pak Tung Ho,