Minimal Surfaces: Integrable Systems and Visualisation

1. Front Matter

   Pages i-viii

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2. Translating Solutions to Mean Curvature Flow

   • Theodora Bourni, Mat Langford, Giuseppe Tinaglia

   Pages 1-12

3. Finding Conformal and Isometric Immersions of Surfaces

   • Albert Chern, Felix Knöppel, Franz Pedit, Ulrich Pinkall, Peter Schröder

   Pages 13-33

4. Discrete Minimal Nets with Symmetries

   • Joseph Cho, Wayne Rossman, Seong-Deog Yang

   Pages 35-50

5. A Survey on Minimal Isometric Immersions into \(\mathbb {R}^3\), \(\mathbb {S}^2\times \mathbb {R}\) and \(\mathbb {H}^2\times \mathbb {R}\)

   • Benoît Daniel

   Pages 51-65

6. Families of Minimal Surfaces in \(\mathbb {H}^2 \times \mathbb {R}\) Foliated by Arcs and Their Jacobi Fields

   • Leonor Ferrer, Francisco Martín, Rafe Mazzeo, Magdalena Rodríguez

   Pages 67-88

7. Jenkins–Serrin Graphs in \(M\times \mathbb {R}\)

   • Eddygledson S. Gama, Esko Heinonen, Jorge H. de Lira, Francisco Martín

   Pages 89-109

8. Survey on the Asymptotic Dirichlet Problem for the Minimal Surface Equation

   • Esko Heinonen

   Pages 111-129

9. Generalized Whitham Flow and Its Applications

   • Lynn Heller

   Pages 131-146

10. Notes on Translating Solitons for Mean Curvature Flow

    • David Hoffman, Tom Ilmanen, Francisco Martín, Brian White

    Pages 147-168

11. Uniqueness Problem for Closed Non-smooth Hypersurfaces with Constant Anisotropic Mean Curvature and Self-similar Solutions of Anisotropic Mean Curvature Flow

    • Miyuki Koiso

    Pages 169-185

12. The Translating Soliton Equation

    • Rafael López

    Pages 187-216

13. Constant Mean Curvature Surfaces for the Bessel Equation

    • Eduardo Mota

    Pages 217-227

14. Minimal Surfaces Under Constrained Willmore Transformation

    • Áurea Casinhas Quintino

    Pages 229-245

15. On an Enneper–Weierstrass-Type Representation of Constant Gaussian Curvature Surfaces in 3-Dimensional Hyperbolic Space

    • Graham Smith

    Pages 247-256

16. Loss of Initial Data Under Limits of Ricci Flows

    • Peter M. Topping

    Pages 257-261

17. Semi-discrete Maximal Surfaces with Singularities in Minkowski Space

    • Masashi Yasumoto

    Pages 263-280

This book collects original peer-reviewed contributions to the conferences organised by the international research network “Minimal surfaces: Integrable Systems and Visualization” financed by the Leverhulme Trust. The conferences took place in Cork, Granada, Munich and Leicester between 2016 and 2019. Within the theme of the network, the presented articles cover a broad range of topics and explore exciting links between problems related to the mean curvature of surfaces in homogeneous 3-manifolds, like minimal surfaces, CMC surfaces and mean curvature flows, integrable systems and visualisation. Combining research and overview articles by prominent international researchers, the book offers a valuable resource for both researchers and students who are interested in this research area.  

• Computer Science
• Informatics
• Conference Proceedings
• Research
• Applications
• surfaces in homogeneous 3-manifolds
• minimal surfaces
• CMC surfaces
• mean curvature flow
• discrete geometry
• visualisation

• Fakultät für Mathematik, Technical University Munich, Garching, Germany

  Tim Hoffmann

• School of Mathematical Sciences, University College Cork, Cork, Ireland

  Martin Kilian

• School of Mathematics & Actuarial Science, University of Leicester, Leicester, UK

  Katrin Leschke

• Department of Geometry & Topology, University of Granada, Granada, Spain

  Francisco Martin

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