Minimal Surfaces: Integrable Systems and Visualisation: m:iv Workshops, 2016–19

Introduction
Proceedings of the Workshop Series of Minimal Surfaces: Integrable Systems and Visualisation
Contents
Translating Solutions to Mean Curvature Flow
1 Introduction
2 Translators
3 Ancient Solutions with Discrete Symmetry Groups
References
Finding Conformal and Isometric Immersions of Surfaces
1 Introduction
2 Spin Bundles and Regular Homotopy Classes
3 Conformal and Isometric Immersions
References
Discrete Minimal Nets with Symmetries
1 Introduction
2 Preliminaries
2.1 Discrete Isothermic Nets
2.2 Discrete Gaussian and Mean Curvatures
2.3 Planar Reflection Principle for Discrete Isothermic Minimal and cmc Nets
3 Reflection Properties of Discrete Minimal Nets
3.1 Discrete Isothermic Minimal Nets
3.2 Discrete Asympotic Minimal Nets
3.3 Reflection Properties of Discrete Minimal Nets
4 Examples of Discrete Minimal Nets with Symmetry
References
A Survey on Minimal Isometric Immersions into mathbbR3, mathbbS2timesmathbbR and mathbbH2timesmathbbR
1 Introduction
2 The Local Problem in mathbbR3
2.1 The Associate Family
2.2 Calabi's Rigidity Result
2.3 The Existence Problem
2.4 Generalizations
3 The Global Problem in mathbbR3
4 The Local Problem in mathbbS2timesmathbbR and mathbbH2timesmathbbR
5 Possible Extensions
References
Families of Minimal Surfaces in mathbbH2 timesmathbbR Foliated by Arcs and Their Jacobi Fields
1 Introduction
2 Preliminaries and Notation
3 Catenoids of Revolution in mathbbH2 timesmathbbR
4 Parabolic Catenoids
5 Tall Rectangles
6 Jacobi Fields on Parabolic Catenoids
6.1 Deformations to Catenoids
6.2 Deformations to Tall Rectangles
7 The Jacobi Operator on Parabolic Catenoids
References
Jenkins–Serrin Graphs in MtimesmathbbR
1 Introduction
2 Compactness Theorem for Stable Integral Varifolds
3 Translating Graphs
3.1 The Euclidean Case
4 Jenkins–Serrin Translating Solitons
References
Survey on the Asymptotic Dirichlet Problem for the Minimal Surface Equation
1 Preliminaries
1.1 Cartan–Hadamard Manifolds
1.2 Asymptotic Dirichlet Problem on Cartan–Hadamard Manifolds
2 Overview of the Results
2.1 Minimal Surfaces
2.2 Other Prescribed Mean Curvature Surfaces
3 Different Strategies to Solve the Asymptotic Dirichlet Problem
3.1 Methods Related to Barriers
3.2 Sobolev and Poincaré Inequalities with Moser Iteration
4 Non-solvability of the Asymptotic Dirichlet Problem
References
Generalized Whitham Flow and Its Applications
1 Introduction
2 The Deligne–Hitchin Moduli Space
2.1 Stability
2.2 Automorphisms of the Deligne–Hitchin Moduli Space
3 Higher Genus CMC Surfaces
3.1 Abelianization
3.2 Deformation of Harmonic Maps
4 Higher Solutions and Constrained Willmore Surfaces
References
Notes on Translating Solitons for Mean Curvature Flow
1 Introduction
2 Some Remarks About Singularities
3 Translators
3.1 Variational Approach
4 Examples of Translators
5 Graphical Translators
6 The Spruck–Xiao Convexity Theorem
7 Characterization of Translating Graphs in R3
References
Uniqueness Problem for Closed Non-smooth Hypersurfaces with Constant Anisotropic Mean Curvature and Self-similar Solutions of Anisotropic Mean Curvature Flow
1 Introduction
2 Preliminaries
2.1 Definitions of Piecewise-Cr Weak Immersion and Its Anisotropic Energy
2.2 Wulff Shape and Convexity of Integrands
3 First Variation Formula, Anisotropic Curvatures, and Anisotropic Gauss Map
4 Outline of the Proof of Theorem 1
5 Examples of Non-convex Integrand and Proofs of Theorems 2 and 3
5.1 A One-Dimensional Example
5.2 Higher Dimensional Examples
5.3 Outline of Proofs of Theorems 2 and 3
6 Anisotropic Mean Curvature Flow
References
The Translating Soliton Equation
1 Historical Introduction and Motivation
2 Examples of Translating Solitons
2.1 Cylindrical Surfaces
2.2 Rotational Surfaces
3 Properties of the Solutions of the Translating Soliton Equation
4 The Dirichlet Problem in Bounded Convex Domains
5 The Dirichlet Problem for the Constant Weighted Mean Curvature
6 The Dirichlet Problem in Unbounded Domains
References
Constant Mean Curvature Surfaces for the Bessel Equation
1 The Generalised Weierstrass Representation
2 The Bessel Equation
3 The zAP Lemma and Perturbations at a Simple Pole
4 Constructing CMC Cylinders
4.1 Cylinder Potential
4.2 Local Gauge
4.3 Unitary Monodromy on the Twice-Puncture Riemann Sphere
4.4 Main Theorem
5 Symmetry
5.1 Cylinders with One Reflection
References
Minimal Surfaces Under Constrained Willmore Transformation
1 Introduction
2 The Willmore Energy
3 Conformal Invariance and the Central Sphere Congruence
4 Constrained Willmore Surfaces and Harmonicity
5 Isothermic Constrained Willmore Surfaces
6 Transformations of Constrained Willmore Surfaces
6.1 Spectral Deformation
6.2 Bäcklund Transformation
7 Polynomial Conserved Quantities for Constrained Willmore Surfaces
8 Transformations of Special Constrained Willmore Surfaces
9 Constant Mean Curvature Surfaces Under Constrained Willmore Transformation
References
On an Enneper–Weierstrass-Type Representation of Constant Gaussian Curvature Surfaces in 3-Dimensional Hyperbolic Space
1 Introduction
1.1 Background
1.2 Main Result
1.3 Labourie's Compactness Theorem
1.4 General Properties of k-Surfaces
1.5 Limit Points of the Immersion
1.6 Limit Points of the Weierstrass Map
1.7 Systoles
References
Loss of Initial Data Under Limits of Ricci Flows
1 Introduction
2 The Construction
References
Semi-discrete Maximal Surfaces with Singularities in Minkowski Space
1 Introduction
1.1 Overview
1.2 Previous Works
1.3 Main Results
2 Semi-discrete Isothermic Surfaces in mathbbR2,1
3 Proof of Theorem 1
4 Examples of Semi-discrete Isothermic Maximal Surfaces
5 Associated Families of Semi-discrete Maximal Surfaces
6 Singularities of Semi-discrete Maximal Surfaces
6.1 Singularities of Semi-discrete Isothermic Maximal Surfaces
6.2 Singularities of Associated Families of Semi-discrete Isothermic Maximal Surfaces
References