Titlebook: Differential Geometry in the Large; Seminar Lectures New Heinz Hopf Book 19831st edition Springer-Verlag Berlin Heidelberg 1983 Geometrie.G

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The Isoperimetric Inequality and Related InequalitiesIn this chapter the isoperimetric inequality and related inequalities will be discussed.

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The Elementary Concept of Area and VolumeIn elementary geometry area (volume) is defined in the following manner:

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声明

Differential Geometry of Surfaces in the Small [summary sketch]The following notation will be used:There will be a “parameter plane”, E., with Cartesian coordinates (u,v) or (u.,u.) and a Euclidean space E. with Cartesian coordinates (x,y,z) or (x.,x.,x.).

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Some General Remarks on Closed Surfaces in Differential GeometryAs a general reference to the topological material covered in this chapter, see Seifert-Threlfall: Lehrbuch der Topologie.

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The Congruence Theorem for OvaloidsLet S and S* be two isometric surfaces (see I, 2.6). Let h be the isometry between S and S* and let u, v be parameters such that X(u,v) and X*(u,v) are corresponding points under the map h . Then S and S* have the same first fundamental forms; i.e. ..

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Lecture Notes in Mathematicshttp://image.papertrans.cn/d/image/278761.jpg