Titlebook: Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm; Hirotaka Fujimoto Book 1993 Springer Fachmedien Wiesbaden 1993 Gauss

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Aspects of Mathematicshttp://image.papertrans.cn/v/image/980341.jpg

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https://doi.org/10.1007/978-3-322-80271-2Gauss map; Minimum; defect relations; differential equation; holomorphic curve; minimal surfaces; modified

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The Gauss map of minimal surfaces in R3,In this section we investigate some basic facts in differential geometry. We begin by recalling some notions concerning a surface . immersed in .., which means that . is a connected, oriented real 2-dimensional differentiate manifold and . is a differentiable map of . into .. which has maximal rank everywhere.

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The Gauss map of complete minimal surfaces in ,Let . = (..,.....): . → .. be a minimal surface immersed in .. and .. the metric on . induced from ... According to (1.2.12) and Definition 4.2.2, the Ricci curvature Ric[..] is nonpositive. We give the following: DEFINITION 5.1.1. The (normalized) . of a minimal surface . is defined by ..

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