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Non-preserved Curvature Conditions Under Constrained Mean Curvature Flows by Cabezas-Rivas, Esther; Miquel, Vicente is a scholarly article available to read on EtoBox.

What is Non-preserved Curvature Conditions Under Constrained Mean Curvature Flows about?

We provide explicit examples which show that mean convexity (i.e. positivity of the mean curvature) and positivity of the scalar curvature are non-preserved curvature conditions for hypersurfaces of the Euclidean space evolving under either the volume- or the area preserving mean curvature flow. The relevance of our examples is that they disprove some statements of the previous literature, overshadow a widespread folklore conjecture about the behaviour of these flows and bring out the discouraging news that a traditional singularity analysis is not possible for constrained versions of the mean curvature flow.

Author

Cabezas-Rivas, Esther; Miquel, Vicente

Published

2014

Language

EN