[geometry-ml:02940] Minimal surface: integrable systems and visualisation: speaker and abstract

[Katsuhiro Moriya]

幾何学分科会メーリングリストの皆様
 
Minimal surface: integrable systems and visualization
のSpring 2017 Workshop  (27th to 29th March 2017 at Cork (Ireland))
http://www2.le.ac.uk/projects/miv/workshop-programme/spring-2017-workshop 
の講演者とアブストラクトをご案内いたします。
http://www2.le.ac.uk/projects/miv/workshop-programme/spring-2017-workshop-speakers
においてアップデートされます。

このプロジェクトはThe Leverhulme Trust (https://www.leverhulme.ac.uk )によりサポートされています。

守屋克洋
筑波大学数理物質系数学域

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Speakers for the Spring 2017 Workshop:

• Benoît Daniel (Université de Lorraine)

• Isabel Fernández (University of Seville)
Title: Surfaces of critical constant mean curvature and harmonics maps.

Abstract: Minimal surfaces (H=0) in euclidean 3-space and Bryant surfaces (H=1) in hyperbolic 3-space are a special family among all the CMC surfaces in spaces forms. Similarly, surfaces of critical CMC in homogenous 3-spaces present a special behavior among all the CMC surfaces. For example, Fernández and Mira found a hyperbolic Gauss map for surfaces in H2xR that turns out to be harmonic for surfaces of critical CMC. Later on, Daniel discovered a Gauss map for surfaces in Heisenberg space that is also harmonic when the mean curvature is critical. However, both definitions are quite different and it was unclear how to extend them to the general setting. In this talk we will review some properties of critical CMC surfaces in homogeneous 3-spaces and present a unified definition of a Gauss map for surfaces in these ambient spaces that is harmonic when the mean curvature of the surface is critical.

• Leonor Ferrer (Universit of Granada) 
Title: Properly embedded minimal annuli in H2 × R

Abstract: In this talk we ask for properly embedded minimal annuli in H2 × R which bound a pair of vertical graphs over ∂∞H2 ≡ S1. We present some compactness results for these surfaces. We also give some existence results for proper, Alexandrov-embedded, minimal annuli. Contrary to what might be expected, we show that, in general, one can not prescribe the two components of the boundary at infinity. However, we can prescribe one of the boundary data, the position of the neck and the vertical flux of the annulus. This is a joint work with F. Martín, R. Mazzeo and M. Rodríguez.

• Sebastian Klein (University College Cork)
• Laurent Hauswirth (Université Paris-Est) 
• Ben McKay (University College Cork)
Title: Isometric immersions and integrability

Abstract: Some examples of surfaces for which isometric immersion to a space form is an integrable system.

• Barbara Nelli (University of L'Aquila)
Title: Minimal Surfaces in the Heisenberg Space

Abstract: We discuss  the behaviour of some minimal surfaces in the Heisenberg space. In particular, we deal with existence and growth of non compact graphs and stability properties.

• Pablo Mira (Technical University of Cartagena, Spain)
Title: Constant mean curvature spheres in homogeneous three-manifolds, I

Abstract: The aim of these two talks (which are based on joint work with Bill Meeks and Antonio Ros) is to prove the following theorem any two spheres of the       same constant mean curvature immersed in a homogeneous three-manifold only differ by an ambient isometry. Ourstudy will also determine the exact values of the mean curvature for which such CMC spheres exist, together with some of their most important geometric properties. For instance, we will show that CMC spheres in simply connected metric Lie groups have index one, are Alexandrov embedded and maximally symmetric, their left invariant Gauss maps are diffeos, and the corresponding moduli space of CMC spheres is a connected one-dimensional manifold.

• Franz Pedit (University of Massachusetts, Amherst) 
• Joaquín Pérez (University of Granada) 
Title: Constant mean curvature spheres in homogeneous three-manifolds, II

Abstract: See Pablo Mira.

• Ulrich Pinkall (Techinical University Berlin)
Title: From Smoke Ring Flow to Real Fluids

Abstract:   The so-called "smoke ring flow" for space curves was introduced in 1910 by Da Rios (who was a PhD student of Levi-Civita) for describing the time evolution of vortex filaments in an ideal fluid. Starting from the 1970's it became clear that the smoke ring flow actually is the most basic integrable system that originates in Differential Geometry. It is closely related to the one-dimensional Landau-Lifshitz equation and to the one-dimensional nonlinear Schrödinger equation. As an asymptotic limit it is also crucial for understanding the geometry of CMC surfaces in space forms.
Vortex filaments are the solitons of fluid dynamics, so in this sense fluid flow can be viewed as a perturbed integrable system. In this talk we will show a method for fluid simulation that reflects this fact. This method is closely related to the three-dimensional  Landau-Lifshitz equation and to the three-dimensional nonlinear Schrödinger equation.

• Martin Schmidt (University of Mannheim)