Global Theory Of Minimal Surfaces

COVER......Page 1
Contents......Page 2
Preface......Page 4
Computational Aspects of Discrete Minimal Surfaces......Page 74
Geometric Measure Theory and the Proof of Double Hubble Conjecture......Page 10
Classical Minimal Surfaces in Euclidean Space by Examples:Geometric and Computational Aspects of the Weierstrass Representation......Page 28
Mean Curvature in Riemannian Geometry and general Relativity......Page 122
Introduction to Conjugate Plateau Constructions......Page 146
Parabolicity and Minimal Surfaces......Page 172
The Isoperimetric Problem......Page 184
Flat Structures, Teichmuller Theory and Handle Addition for Minimal Surfaces......Page 220
The Genus-One Helicoid as a Limit of Screw-Motion Invariant Helicoids with Handles......Page 252
Computing Minimal Surfaces......Page 268
Geometric Aspects of the Theory of Fully Nonlinear Elliptic Equations......Page 292
Hyperbolic Surfaces of Constant Mean Curvature One with Compact Fundamental Domains......Page 320
Isoperimetric Inequalities of Minimal Submanifolds......Page 334
Complete Nonorientable Minimal Surfaces in R(3)......Page 380
Some Picard-Type Results for Properly Immersed Minimal Surfaces in R(3)......Page 390
Optimal Isoperimetric Inequalities for Three-Dimensional Cartan-Hadamard Manifolds......Page 404
Embedded Minimal Disks......Page 414
Construction of Minimal Surfaces by Gluing Weierstrass Representations......Page 448
Global Problems in Classical Minimal Surface Theory......Page 462
Minimal Surfaces of Finite Topology......Page 480
Constructions of Minimal Surfaces......Page 498
The Conformal Theory of Alexandrov Embedded Constant Mean Curvature Surfaces in R(3)......Page 534
Constructing Mean Curvature 1 Surfaces in H(3) with Irregular Ends......Page 570
Conformal Structures and Necksizes of Embedded Constant Mean Curvature Surfaces......Page 594
The Mathematical Protein Folding Problem......Page 606
Minimal and CMC Surfaces Obtained by Ribaucour Transformations......Page 632
Meromorphic Data for Surfaces of Mean Curvature One in Hyperbolic Space II......Page 644
Special Lagrangian Submanifolds......Page 664
Lectures on Special Lagrangian Geometry......Page 676
Variational Problems in Lagrangian Geometry: Z(2)-Currents......Page 706
minimal Surfaces and the Topology of Three-Manifolds......Page 714
Minimal Surfaces in Geometric 3-Manifolds......Page 734
Cousins of Constant Mean Curvature Surfaces......Page 756
An Approach to the Willmore Conjecture......Page 778
Minimal Surfaces and Harmonic Maps into Singular Geometry......Page 782
Shortest Networks in 2 and 3 Dimensions......Page 792
List of Participants......Page 800