Boundary Behaviour of Minimal Surfaces / Part I: |
Minimal Surfaces with Free Boundaries / Chapter 1: |
Classes of Admissible Functions. Linking Condition / 1.1: |
Existence of Minimizers for the Free Boundary Problem / 1.3: |
Stationary Minimal Surfaces with Free or Partially Free Boundaries and the Transversality Condition / 1.4: |
Necessary Conditions for Stationary Minimal Surfaces / 1.5: |
Existence of Stationary Minimal Surfaces in a Simplex / 1.6: |
Stationary Minimal Surfaces of Disk-Type in a Sphere / 1.7: |
Report on the Existence of Stationary Minimal Surfaces in Convex Bodies / 1.8: |
Nonuniqueness of Solutions to a Free Boundary Problem. Families of Solutions / 1.9: |
Scholia / 1.10: |
The Boundary Behaviour of Minimal Surfaces / Chapter 2: |
Potential-Theoretic Preparations / 2.1: |
Solutions of Differential Inequalities / 2.2: |
The Boundary Regularity of Minimal Surfaces Bounded by Jordan Arcs / 2.3: |
The Boundary Behaviour of Minimal Surfaces at Their Free Boundary: A Survey of the Results and an Outline of Their Proofs / 2.4: |
Hölder Continuity for Minima / 2.5: |
Hölder Continuity for Stationary Surfaces / 2.6: |
Higher Regularity in Case of Support Surfaces with Empty Boundaries. Analytic Continuation Across a Free Boundary / 2.7: |
A Different Approach to Boundary Regularity / 2.9: |
Asymptotic Expansion of Minimal Surfaces at Boundary Branch Points and Geometric Consequences / 2.10: |
The Gauss-Bonnet Formula for Branched Minimal Surfaces / 2.11: |
Singular Boundary Points of Minimal Surfaces / 2.12: |
The Method of Hartman and Wintner, and Asymptotic Expansions at Boundary Branch Points / 3.1: |
A Gradient Estimate at Singularities Corresponding to Corners of the Boundary / 3.2: |
Minimal Surfaces with Piecewise Smooth Boundary Curves and their Asymptotic Behaviour at Corners / 3.3: |
An Asymptotic Expansion for Solutions of the Partially Free Boundary Problem / 3.4: |
References / 3.5: |
Hölder Continuity at Intersection Points / 3.5.2: |
Geometric Properties of Minimal Surfaces and H-Surfaces / Part II: |
Enclosure and Existence Theorems for Minimal Surfaces and H-Surfaces. Isoperimetric Inequalities / Chapter 4: |
Applications of the Maximum Principle and Nonexistence of Multiply Connected Minimal Surfaces with Prescribed Boundaries / 4.1: |
Touching H-Surfaces and Enclosure Theorems. Further Nonexistence Results / 4.2: |
Minimal Submanifolds and Submanifolds of Bounded Mean Curvature. An Optimal Nonexistence Result / 4.3: |
An Optimal Nonexistence Result for Minimal Submanifolds of Codimension One / 4.3.1: |
Geometric Maximum Principles / 4.4: |
The Barrier Principle for Submanifolds of Arbitrary Codimension / 4.4.1: |
A Geometric Inclusion Principle for Strong Subsolutions / 4.4.2: |
Isoperimetric Inequalities / 4.5: |
Estimates for the Length of the Free Trace / 4.6: |
Obstacle Problems and Existence Results for Surfaces of Prescribed Mean Curvature / 4.7: |
Surfaces of Prescribed Mean Curvature in a Riemannian Manifold / 4.8: |
Estimates for Jacobi Fields / 4.8.1: |
Riemann Normal Coordinates / 4.8.2: |
Enclosure Theorems and Nonexistence / 4.8.3: |
The Isoperimetric Problem. Historical Remarks and References to the Literature / 4.9.2: |
Experimental Proof of the Isoperimetric Inequality / 4.9.3: |
The Plateau Problem for H-Surfaces / 4.9.4: |
The Thread Problem / Chapter 5: |
Experiments and Examples. Mathematical Formulation of the Simplest Thread Problem / 5.1: |
Existence of Solutions to the Thread Problem / 5.2: |
Analyticity of the Movable Boundary / 5.3: |
Branch Points / 5.4: |
The First Five Variations of Dirichlet's Integral, and Forced Jacobi Fields / 6.1: |
The Theorem for n + 1 Even and m + 1 Odd / 6.2: |
Boundary Branch Points / 6.3: |
Bibliography / 6.4: |
Index |
Boundary Behaviour of Minimal Surfaces / Part I: |
Minimal Surfaces with Free Boundaries / Chapter 1: |
Classes of Admissible Functions. Linking Condition / 1.1: |
Existence of Minimizers for the Free Boundary Problem / 1.3: |
Stationary Minimal Surfaces with Free or Partially Free Boundaries and the Transversality Condition / 1.4: |
Necessary Conditions for Stationary Minimal Surfaces / 1.5: |