Titlebook: Generalized Curvatures; Jean-Marie Morvan Book 2008 Springer-Verlag Berlin Heidelberg 2008 Gaussian curvature.Riemannian geometry.Riemanni

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Currentsrt introduction to this subject. We end this chapter with important theorems used in the approximation and convergence results proved in the succeeding parts of the book. A nice introduction to this subject can be found in [63].

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Jean-Marie MorvanFirst coherent and complete account of this subject in book form

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https://doi.org/10.1007/978-1-4612-4772-2Our goal in this chapter is to point out the difficulties arising when one evaluates the area and the curvatures of a surface by approximation.

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K. E. Kürten,M. L. Ristig,J. W. ClarkThere is an abundant literature on convexity, crucial in many fields of mathematics. We shall mention the basic definitions and some fundamental results (without proof), useful for our topic. In particular, we shall focus on the properties of the volume of a convex body and its boundary. The reader can consult [9, 71, 74, 79] for details.

鍍金

ALLAY

J. N. Herrera,L. Blum,Fernando VericatLet us introduce the concept of . on a .-manifold . of dimension . with or without boundary ?. (.≥1,.≥2). The goal is to use suitable differential forms to construct measures, with which one can define the notion of ., fundamental in our context. Chapter 3 of [11] gives a complete introduction to the subject.

不透明性

Situation, Jetztsein, Psychose,We have seen in Chap. 13 that the length of a curve is classically defined as the supremum of the lengths of polygonal lines inscribed in it. Our purpose here is to compare the length of a given smooth curve with the length of a curve close to it, or more precisely with the length of a polygonal line inscribed in it.

Indelible

MAOIS

Hédi Hamdi,Charfeddine Mrad,Rachid NasriIn previous chapters, we have seen that it is possible to define . which describe the global shape of two classes of subsets of E., namely the convex bodies and the smooth submanifolds. A good challenge is to find larger classes of subsets on which a more general theory holds. In 1958, Federer [43] made a major advance in two directions:

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