TOPICS
Search

Tangent Flow


A tangent flow at a singular space-time point (x_0,T) of mean curvature flow is a limit of parabolically dilated flows about that point. For a positive dilation factor lambda, write

 M_s^lambda=lambda(M_(T+lambda^(-2)s)-x_0),

where s<0 describes times before the singularity. A tangent flow is obtained along a sequence lambda->infty when a limit exists in the specified topology. Its center and spatial axes are fixed by this rescaling. Uniqueness asserts independence of the sequence.


See also

Mean Curvature Flow, Self-Shrinker

Explore with Wolfram|Alpha

References

Colding, T. H. and Minicozzi, W. P., II. "Generic Mean Curvature Flow I; Generic Singularities." Ann. Math. 175, 755-833, 2012. https://doi.org/10.4007/annals.2012.175.2.7.Simons, J. "Minimal Varieties in Riemannian Manifolds." Ann. Math. 88, 62-105, 1968. https://doi.org/10.2307/1970556.

Cite this as:

Weisstein, Eric W. "Tangent Flow." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TangentFlow.html

Subject classifications