R^3中的完備極小子流形
COMPLETE MINIMAL SUBMANIFOLDS IN R^3
Date Issued
2004
Date
2004
Author(s)
Hsu, Yu-Chin
DOI
en-US
Abstract
There are seven sections in this paper. In the first one, we introduce what we mean by a minimal surface. In the second, a powerful tool for constructing minimal surfaces is given, and then, in the third, some minimal surfaces are constructed from it and the definition of a complete minimal surface is given, too. In the fourth, the properties of the Gauss maps of complete minimal surfaces are discussed. In the fifth, by Osserman's theorem, we focus our attation on complete minimal surfaces with finite total curvature at first, and then pay attation to the characters of ends. In the sixth, there are some classifications of complete minimal surfaces with finite total curvature and some conditions which imply the nonexistence of complete minimal surfaces. In the last one, a more variety of surfaces than section 3 are given, and finally we list surfaces in tables to make some comparisons.
Subjects
極小子流形
MINIMAL SUBMANIFOLDS
Type
thesis
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