The authors study noncompact surfaces evolving by mean curvature flow (mcf). For an open set of initial data that are $C^3$-close to round, but without assuming rotational symmetry or positive mean curvature, the authors show that mcf solutions become singular in finite time by forming neckpinches, and they obtain detailed asymptotics of that singularity formation. The results show in a precise way that mcf solutions become asymptotically rotationally symmetric near a neckpinch singularity.
- ISBN13 9781470428402
- Publish Date 1 May 2018
- Publish Status Active
- Publish Country US
- Imprint American Mathematical Society
- Format Paperback
- Pages 78
- Language English