5 Constrained Willmore Surfaces
نویسنده
چکیده
We develop the basics of a theory of constrained Willmore surfaces. These are the critical points of the Willmore functional W = ∫ HdA restricted to the class of conformal immersions of a fixed Riemann surface. The class of constrained Willmore surfaces is invariant under Möbius transformations of the ambient space. Examples include all constant mean curvature surfaces in space forms.
منابع مشابه
Constrained Willmore Surfaces
The aim of this article is to develop the basics of a theory of constrained Willmore surfaces. These are the critical points of the Willmore functional W = ∫ H 2 dA restricted to the class of conformal immersions of a fixed Riemann surface. The class of constrained Willmore surfaces is invariant under Möbius transformations of the ambient space. Examples include all constant mean curvature surf...
متن کامل2 00 8 Constrained Willmore Surfaces
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy W = R H 2 under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the critical points of arbitrary geometric functionals on the space of immersions under ...
متن کاملNew Examples of Willmore Surfaces in Sn
A surface x : M ! S n is called a Willmore surface if it is a critical surface of the Willmore functional R M (S ? 2H 2)dv, where H is the mean curvature and S is the square of the length of the second fundamental form. It is well-known that any minimal surface is a Willmore surface. The rst non-minimal example of a at Willmore surface in higher codimension was obtained by Ejiri. This example w...
متن کاملA Nested Variational Time Discretization for Parametric Willmore Flow
A novel variational time discretization of isotropic and anisotropic Willmore flow combined with a spatial parametric finite element discretization is applied to the evolution of polygonal curves and triangulated surfaces. In the underlying natural approach for the discretization of gradient flows a nested optimization problem has to be solved at each time step. Thereby, an outer variational pr...
متن کاملTwo Step Time Discretization of Willmore Flow
Based on a natural approach for the time discretization of gradient flows a new time discretization for discrete Willmore flow of polygonal curves and triangulated surfaces is proposed. The approach is variational and takes into account an approximation of the L-distance between the surface at the current time step and the unknown surface at the new time step as well as a fully implicity approx...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005