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Gradient Estimates for Spacelike Mean Curvature Flow with Boundary Conditions

Part of: Parabolic equations and systems Global differential geometry

Published online by Cambridge University Press:  29 November 2018

Ben Lambert
Ben Lambert*
Affiliation:
25 Gordon Street, London WC1H 0AY, UK (b.lambert@ucl.ac.uk)
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Abstract

We prove a gradient estimate for graphical spacelike mean curvature flow with a general Neumann boundary condition in dimension n = 2. This then implies that the mean curvature flow exists for all time and converges to a translating solution.

Keywords

mean curvature flowgradient estimatesNeumann boundary conditionssemi-Riemannian geometryquasi-linear PDEs

MSC classification

Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 53C50: Lorentz manifolds, manifolds with indefinite metrics 35K59: Quasilinear parabolic equations 35K20: Initial-boundary value problems for second-order parabolic equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 2 , May 2019 , pp. 459 - 469
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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