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Minimal Surfaces: Integrable Systems and Visualisation

m:iv Workshops, 2016–19

  • Conference proceedings
  • © 2021

Overview

Editors:
  1. Tim Hoffmann

    1. Fakultät für Mathematik, Technical University Munich, Garching, Germany

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  2. Martin Kilian

    1. School of Mathematical Sciences, University College Cork, Cork, Ireland

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  3. Katrin Leschke

    1. School of Mathematics & Actuarial Science, University of Leicester, Leicester, UK

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  4. Francisco Martin

    1. Department of Geometry & Topology, University of Granada, Granada, Spain

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  • Combines research and overview articles by world-leading researchers
  • Provides a valuable resource for researchers and students in differential geometry, discrete geometry and visualisation
  • Includes relevant results on several problems related with the mean curvature of surfaces in homogeneous 3-manifolds, like minimal surfaces, CMC surfaces and mean curvature flows, among others

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 349)

Included in the following conference series:

Conference proceedings info: m:iv 2017. m:iv 2018. m:iv 2018. m:iv 2019.

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Table of contents (16 papers)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  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
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  1. Minimal Surfaces: Integrable Systems and Visualisation

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About this book

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.  

Editors and Affiliations

  • 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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