Lecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations

Table of Contents

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   Book Overview
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   Chapter 1 Signed distance from a smooth boundary
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   Chapter 2 First variations
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   Chapter 3 Smooth flows
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   Chapter 4 Huisken’s monotonicity formula
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   Chapter 5 Inclusion principle
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   Chapter 6 Extension of the evolution equation to a neighbourhood
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   Chapter 7 Local well-posedness: the approach of Evans and Spruck
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   Chapter 8 Grayson’s example
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    Chapter 9 De Giorgi’s barriers
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    Chapter 10 Inner and outer regularizations
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    Chapter 11 An example of fattening
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    Chapter 12 Ilmanen’s interposition lemma
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    Chapter 13 The avoidance principle
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    Chapter 14 Comparison between barriers and a generalized evolution
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    Chapter 15 One-dimensional analysis related to a reaction-diffusion equation
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    Chapter 16 Parabolic singular perturbations: formal matched asymptotics
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    Chapter 17 Parabolic singular perturbations: convergence and error estimate