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