Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589598 | Journal of Functional Analysis | 2016 | 27 Pages |
Abstract
We show that the norm of the Riemann curvature tensor of any smooth solution to the Ricci flow can be explicitly estimated in terms of its initial values on a given ball, a local uniform bound on the Ricci tensor, and the elapsed time. This provides a new, direct proof of a result of Šesǔm, which asserts that the curvature of a solution on a compact manifold cannot blow up while the Ricci curvature remains bounded, and extends its conclusions to the noncompact setting. We also prove that the Ricci curvature must blow up at least linearly along a subsequence at a finite time singularity.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Brett Kotschwar, Ovidiu Munteanu, Jiaping Wang,