The Space of Complete Minimal Surfaces with Finite Total Curvature as Lagrangian Submanifold
نویسنده
چکیده
The spaceM of nondegenerate, properly embedded minimal surfaces in R3 with finite total curvature and fixed topology is an analytic lagrangian submanifold of Cn, where n is the number of ends of the surface. In this paper we give two expressions, one integral and the other pointwise, for the second fundamental form of this submanifold. We also consider the compact boundary case, and we show that the space of stable nonflat minimal annuli that bound a fixed convex curve in a horizontal plane, having a horizontal end of finite total curvature, is a locally convex curve in the plane C.
منابع مشابه
On a Minimal Lagrangian Submanifold of C Foliated by Spheres
In general, not much is known about minimal submanifolds of Euclidean space of high codimension. In [1], Anderson studies complete minimal submanifolds of Euclidean space with finite total scalar curvature, trying to generalize classical results of minimal surfaces. More recently, Moore [10] continues the study of this kind of minimal submanifolds. Harvey and Lawson [6] also study a particular ...
متن کاملJ ul 2 00 9 Uniform Approximation by Algebraic Minimal Surfaces in
An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in R is obtained. This result can be extended to the family of complete minimal surfaces of weak finite total curvature, that is to say, having finite total curvature on proper regions of finite conformal type. We deal only with the orientable case. As a consequence, complete minimal surfaces in...
متن کاملM ar 2 00 9 Uniform Approximation by Algebraic Minimal Surfaces in R 3
An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in R is obtained. This result can be extended to the family of complete minimal surfaces of weak finite total curvature, that is to say, having finite total curvature on proper regions of finite conformal type. We deal only with the orientable case. As a consequence, complete minimal surfaces in...
متن کاملM ar 2 00 9 Uniform Approximation by Algebraic Minimal Surfaces in R 3 Francisco
An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in R is obtained. This result can be extended to the family of complete minimal surfaces of weak finite total curvature, that is to say, having finite total curvature on proper regions of finite conformal type. We deal only with the orientable case. As a consequence, complete minimal surfaces in...
متن کاملar X iv : 0 90 3 . 32 09 v 1 [ m at h . D G ] 1 8 M ar 2 00 9 Uniform Approximation by Algebraic Minimal Surfaces in R 3
An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in R is obtained. This result can be extended to the family of complete minimal surfaces of weak finite total curvature, that is to say, having finite total curvature on proper regions of finite conformal type. We deal only with the orientable case. As a consequence, complete minimal surfaces in...
متن کامل