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Cylindrical estimates
for hypersurfaces moving by convex curvature functions
Ben Andrews and Mat Langford |
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Vol. 7 (2014), No. 5, 1091–1107
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Abstract |
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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 -convex () solution either becomes strictly -convex or its Weingarten map becomes that of a cylinder . This result complements the convexity estimate we proved with McCoy [Anal. PDE 7:2 (2014), 407–433] for the same class of flows. |
Keywords
curvature flows, cylindrical estimates, fully nonlinear,
convexity estimates
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Mathematical Subject Classification 2010
Primary: 53C44, 35K55, 58J35
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Milestones
Received: 8 October 2013
Accepted: 30 June 2014
Published: 27 September 2014
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Authors |
| Ben Andrews | |
| Mathematical Sciences
Institute Australian National University ACT 0200 Australia |
Mathematical Sciences Center Tsinghua University Beijing 100084 China |
| Mat Langford | |
| Mathematical Sciences
Institute Australian National University ACT 0200 Australia |
Fachbereich Mathematik und
Statistik Universität Konstanz 78457 Konstanz Germany |
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