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Preface
Chapter 1£® The Beginning of the Theory
1£®The Minimal Surface Equation and Minimal Submanifolds
2£®Examples of Minimal Surfaces in R3
3£®Consequences of the First Variation Formula
4£®The Gauss Map
5£®The Theorem of Bernstein
6£®The Weierstrass Representation
7£®The Strong Maximum Principle
8£®Second Variation Formula£¬ Morse Index£¬ and Stability
9£®Multi-valued Graphs
10£®Local Examples of Multi-valued Graphs
Appendix£º The Harnack Inequality
Appendix£º The Bochner formula

Chapter 2£® Curvature Estimates and Consequences
1£®Simons'Inequality
2£®Small Energy Curvature Estimates for Minimal Surfaces
3£®Curvature and Area
4£®Lp Bounds of |A|2 for Stable Hypersurfaces
5£®Bernstein Theorems and Curvature Estimates
6£®The General Minimal Graph Equation
7£®Almost Stability
8£®Sublinear Growth of the Separation
9£®Minimal Cones

Chapter 3£® Weak Convergence£¬ Compactness and Applications
1£®The Theory of Varifolds
2£®The Sobolev Inequality
3£®The Weak Bernstein-Type Theorem
4£®General Constructions
5£®Finite Dimensionality
6£®Bubble Convergence Implies Varifold Convergence

Chapter 4£® Existence Results
1£®The Plateau Problem
2£®The Dirichlet£¬ Problem
3£®The Solution to the Plateau Problem
4£®Branch Points
5£®Harmonic Maps
6£®Existence of Minimal Spheres in a Homotopy Class

Chapter 5£® Min-max Constructions
1£®Sweepouts by Curves
2£®Birkhoff's Curve Shortening Process
3£®Existence of Closed Geodesics and the Width
4£®Harmonic Replacement
5£®Minimal Spheres and the Width

Chapter 6£® Embedded Solutions of the Plateau problem
1£®Unique Continuation
2£®Local Description of Nodal and Critical Sets
3£®Absence of True Branch Points
4£®Absence of False Branch Points
5£®Embedded Solutions of the Plateau Problem

Chapter 7£® Minimal Surfaces in Three-Manifolds
1£®The Minimal Surface Equation in a Three-Manifold
2£®Hersch's and Yang and Yau's Theorems
3£®The Reilly Formula
4£®Choi and Wang's Lower Bound for ¦Ë1
5£®Compactness Theorems with A Priori Bounds
6£®The Positive Mass Theorem
7£®Extinction of Ricci Flow

Chapter 8£® The Structure of Embedded Minimal Surfaces
1£®Disks that are Double-spiral Staircases
2£®One-sided Curvature Estimate
3£®Generalized Nitsche Conjecture
4£®Calabi-Yau Conjectures for Embedded Surfaces
5£®Embedded Minimal Surfaces with Finite Genus
Exercises
Bibliography
Index