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Cylindrical estimates for hypersurfaces moving by convex curvature functions

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2014

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Andrews, Ben

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https://doi.org/10.2140/apde.2014.7.1091
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Analysis & PDE. 2014, 7(5), pp. 1091-1107. ISSN 2157-5045. eISSN 1948-206X. Available under: doi: 10.2140/apde.2014.7.1091

Zusammenfassung

We prove a complete family of cylindrical estimates for solutions of a class of fully nonlinear curvature flows, generalising the cylindrical estimate of Huisken and Sinestrari [Invent. Math. 175:1 (2009), 1–14, §5] for the mean curvature flow. More precisely, we show, for the class of flows considered, that, at points where the curvature is becoming large, an (m+1)-convex (0≤m≤n−2) solution either becomes strictly m-convex or its Weingarten map becomes that of a cylinder Rm×Sn−m. This result complements the convexity estimate we proved with McCoy [Anal. PDE 7:2 (2014), 407–433] for the same class of flows.

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Fachgebiet (DDC)
510 Mathematik

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curvature flows, cylindrical estimates, fully nonlinear, convexity estimates

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ISO 690ANDREWS, Ben, Mat LANGFORD, 2014. Cylindrical estimates for hypersurfaces moving by convex curvature functions. In: Analysis & PDE. 2014, 7(5), pp. 1091-1107. ISSN 2157-5045. eISSN 1948-206X. Available under: doi: 10.2140/apde.2014.7.1091
BibTex
@article{Andrews2014Cylin-30117,
  year={2014},
  doi={10.2140/apde.2014.7.1091},
  title={Cylindrical estimates for hypersurfaces moving by convex curvature functions},
  number={5},
  volume={7},
  issn={2157-5045},
  journal={Analysis & PDE},
  pages={1091--1107},
  author={Andrews, Ben and Langford, Mat}
}
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