Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow

Released on by Zhou Gang
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  • Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow Book Detail

  • Author : Zhou Gang
  • Release Date : 2018-05-29
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 90
  • ISBN 13 : 1470428407
  • File Size : 98,98 MB
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Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow by Zhou Gang PDF Summary

Book Description: 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.

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The Ricci Flow: Techniques and Applications

The Ricci Flow: Techniques and Applications

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Ricci flow is a powerful technique using a heat-type equation to deform Riemannian metrics on manifolds to better metrics in the search for geometric decomposit