Annals of Mathematics· 2012Q1
Generic mean curvature flow I; generic singularities
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- Q1SCImago
- 2012year
Short summary
Mean curvature flow of generic surfaces in R3 results in singularities that are either spherical or cylindrical.
AI-generated from the title and abstract; the full text is not read.
Key points
- Mean curvature flow of generic smooth closed embedded surfaces in R3 is studied.
- The flow is proven to remain smooth until it reaches a singularity.
- The only possible singularities are spherical or cylindrical.
AI-generated from the title and abstract; the full text is not read.
Abstract
It has long been conjectured that starting at a generic smooth closed embedded surface in R 3 , the mean curvature flow remains smooth until it arrives at a singularity in a neighborhood of which the flow looks like concentric spheres or cylinders. That is, the only singularities of a generic flow are spherical or cylindrical. We will address this conjecture here and in a sequel. The higher dimensional case will be addressed elsewhere.
The authors' abstract, as published at the source. Annals of Mathematics, 2012 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics