Boundary Behaviour of Minimal Surfaces | |
Minimal Surfaces with Free Boundaries | p. 3 |
Surfaces of Class H21 and Homotopy Classes of Their Boundary Curves. Nonsolvability of the Free Boundary Problem with Fixed Homotopy Type of the Boundary Traces | p. 5 |
Classes of Admissible Functions. Linking Condition | p. 18 |
Existence of Minimizers for the Free Boundary Problem | p. 21 |
Stationary Minimal Surfaces with Free or Partially Free Boundaries and the Transversality Condition | p. 28 |
Necessary Conditions for Stationary Minimal Surfaces | p. 35 |
Existence of Stationary Minimal Surfaces in a Simplex | p. 39 |
Stationary Minimal Surfaces of Disk-Type in a Sphere | p. 41 |
Report on the Existence of Stationary Minimal Surfaces in Convex Bodies | p. 43 |
Nonuniqueness of Solutions to a Free Boundary Problem. Families of Solutions | p. 45 |
Scholia | p. 65 |
The Boundary Behaviour of Minimal Surfaces | p. 75 |
Potential-Theoretic Preparations | p. 76 |
Solutions of Differential Inequalities | p. 90 |
The Boundary Regularity of Minimal Surfaces Bounded by Jordan Arcs | p. 102 |
The Boundary Behaviour of Minimal Surfaces at Their Free Boundary: A Survey of the Results and an Outline of Their Proofs | p. 112 |
Hölder Continuity for Minima | p. 118 |
Hölder Continuity for Stationary Surfaces | p. 130 |
C1,1/2-Regularity | p. 153 |
Higher Regularity in Case of Support Surfaces with Empty Boundaries. Analytic Continuation Across a Free Boundary | p. 174 |
A Different Approach to Boundary Regularity | p. 181 |
Asymptotic Expansion of Minimal Surfaces at Boundary Branch Points and Geometric Consequences | p. 189 |
The Gauss-Bonnet Formula for Branched Minimal Surfaces | p. 193 |
Scholia | p. 200 |
Singular Boundary Points of Minimal Surfaces | p. 213 |
The Method of Hartman and Wintner, and Asymptotic Expansions at Boundary Branch Points | p. 214 |
A Gradient Estimate at Singularities Corresponding to Corners of the Boundary | p. 235 |
Minimal Surfaces with Piecewise Smooth Boundary Curves and their Asymptotic Behaviour at Corners | p. 245 |
An Asymptotic Expansion for Solutions of the Partially Free Boundary Problem | p. 259 |
Scholia | p. 271 |
References | p. 271 |
Hölder Continuity at Intersection Points | p. 271 |
Geometric Properties of Minimal Surfaces and H-Surfaces | |
Enclosure and Existence Theorems for Minimal Surfaces and H-Surfaces. Isoperimetric Inequalities | p. 279 |
Applications of the Maximum Principle and Nonexistence of Multiply Connected Minimal Surfaces with Prescribed Boundaries | p. 280 |
Touching H-Surfaces and Enclosure Theorems. Further Nonexistence Results | p. 284 |
Minimal Submanifolds and Submanifolds of Bounded Mean Curvature. An Optimal Nonexistence Result | p. 295 |
An Optimal Nonexistence Result for Minimal Submanifolds of Codimension One | p. 311 |
Geometric Maximum Principles | p. 314 |
The Barrier Principle for Submanifolds of Arbitrary Codimension | p. 314 |
A Geometric Inclusion Principle for Strong Subsolutions | p. 322 |
Isoperimetric Inequalities | p. 332 |
Estimates for the Length of the Free Trace | p. 346 |
Obstacle Problems and Existence Results for Surfaces of Prescribed Mean Curvature | p. 371 |
Surfaces of Prescribed Mean Curvature in a Riemannian Manifold | p. 407 |
Estimates for Jacobi Fields | p. 408 |
Riemann Normal Coordinates | p. 418 |
Surfaces of Prescribed Mean Curvature in a Riemannian Manifold | p. 424 |
Scholia | p. 431 |
Enclosure Theorems and Nonexistence | p. 431 |
The Isoperimetric Problem. Historical Remarks and References to the Literature | p. 433 |
Experimental Proof of the Isoperimetric Inequality | p. 435 |
Estimates for the Length of the Free Trace | p. 435 |
The Plateau Problem for H-Surfaces | p. 437 |
The Thread Problem | p. 441 |
Experiments and Examples. Mathematical Formulation of the Simplest Thread Problem | p. 441 |
Existence of Solutions to the Thread Problem | p. 446 |
Analyticity of the Movable Boundary | p. 463 |
Scholia | p. 483 |
Branch Points | p. 487 |
The First Five Variations of Dirichlet's Integral, and Forced Jacobi Fields | p. 488 |
The Theorem for n + 1 Even and m + 1 Odd | p. 519 |
Boundary Branch Points | p. 528 |
Scholia | p. 554 |
Bibliography | p. 561 |
Index | p. 619 |
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