Reflection of Willmore Surfaces with Free Boundaries
نویسندگان
چکیده
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 کاملAnalysis Aspects of Willmore Surfaces
Abstract : We found a new formulation to the Euler-Lagrange equation of the Willmore functional for immersed surfaces in R. This new formulation of Willmore equation appears to be of divergence form, moreover, the nonlinearities are made of jacobians. Additionally to that, if ~ H denotes the mean curvature vector of the surface, this new form writes L ~ H = 0 where L is a well defined locally i...
متن کامل5 Constrained Willmore Surfaces
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.
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 کاملWillmore Surfaces of Constant Möbius Curvature
We study Willmore surfaces of constant Möbius curvature K in S. It is proved that such a surface in S must be part of a minimal surface in R or the Clifford torus. Another result in this paper is that an isotropic surface (hence also Willmore) in S of constant K could only be part of a complex curve in C ∼= R or the Veronese 2-sphere in S. It is conjectured that they are the only examples possi...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2020
ISSN: 0008-414X,1496-4279
DOI: 10.4153/s0008414x20000164