Correction to: "Complete surfaces of finite total curvature"
نویسندگان
چکیده
منابع مشابه
Complete Embedded Minimal Surfaces of Finite Total Curvature
2 Basic theory and the global Weierstrass representation 4 2.1 Finite total curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 The example of Chen-Gackstatter . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 Embeddedness and finite total curvature: necessary conditions . . . . . . . 20 2.3.1 Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملModern Examples of Complete Embedded Minimal Surfaces of Finite Total Curvature
1. Introduction. A natural class of minimal surfaces to study are the embedded mini mal surfaces — those which have no selfintersections as a subset of R 3. Of course, every point of a surface immersed in R 3 has a neighborhood which is embedded, so by itself this isn't a very interesting restriction. However, an embedded minimal surface pro duced in this way is clearly extendable and thus n...
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An approximation theorem for compact minimal surfaces by complete minimal surfaces of finite total curvature in R is obtained. This Mergelyan type 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 regions of finite conformal type. We deal only with the orientable case.
متن کاملThe Space of Complete Minimal Surfaces with Finite Total Curvature as Lagrangian Submanifold
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 tha...
متن کاملj differential geometry COMPLETE EMBEDDED MINIMAL SURFACES OF FINITE TOTAL CURVATURE
A general construction for complete embedded minimal surfaces of nite total curvature in Euclidean three space is carried out In particular ex amples with an arbitrary number of ends are given for the rst time The construction amounts to desingularizing the circles of intersection of a col lection of coaxial catenoids and planes The desingularization process uses Scherk s singly periodic surfac...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1988
ISSN: 0022-040X
DOI: 10.4310/jdg/1214442284