Abstract
We prove two new estimates for the level set flow of mean convex domains in Riemannian manifolds. Our estimates give control – exponential in time – for the infimum of the mean curvature, and the ratio between the norm of the second fundamental form and the mean curvature. In particular, the estimates remove a stumbling block that has been left after the work of White [16,17,20], and Haslhofer–Kleiner [9], and thus allow us to extend the structure theory for mean convex level set flow to general ambient manifolds of arbitrary dimension.
Original language | American English |
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Pages (from-to) | 1137-1155 |
Number of pages | 19 |
Journal | Advances in Mathematics |
Volume | 329 |
DOIs | |
State | Published - 30 Apr 2018 |
Externally published | Yes |
Bibliographical note
Funding Information:Acknowledgments. We thank Brian White for bringing the problem of subsequent singularities in Riemannian manifolds to our attention. This work has been partially supported by the NSF grants DMS-1406394 and DMS-1406407. The second author wishes to thank Jeff Cheeger for his generous support during the work on this project.
Publisher Copyright:
© 2018 Elsevier Inc.
Keywords
- Level set flow
- Mean curvature flow