Titlebook: Geometric Inequalities; Yuri? Dmitrievich Burago,Viktor Abramovich Zalgall Book 1988 Springer-Verlag Berlin Heidelberg 1988 Mean curvature

erythema

J?rg Schüttrumpf,Matthias Germert], [Eis], [Ras], [BiC], [KoN], [Sp], [Wo], [GKM], [dCar], [GLP], [K 1]. Our notations are closer to [GKM]. The variational theory of geodesics is used in an essential way. Its exposition may be found in the books [Mil 2], [Pos]. Comparison theorems are developed in part in [GKM], [K 1], [ChE], [BiC

下船

Anti-atherosclerotic activity1,The area F and the length L of any plane domain with rectifiable boundary satisfy the inequality . the equality sign holds only in the case of a circle.

河流

Pharmacological Models in Dermatology,To every pair of non-empty sets ., . ? ?. their (vector) Minkowski . is defined by . + . = {. + .: . ∈ ., . ∈ .}. If ., . are compact sets (i.e. bounded closed sets), then . is compact. In this case each of the sets ., ., . necessarily has a volume (its Lebesgue measure). Denote these volumes by .(.), .(.), .(.).

清洗

無價值

明確

The Brunn-Minkowski Inequality and the Classical Isoperimetric Inequality,To every pair of non-empty sets ., . ? ?. their (vector) Minkowski . is defined by . + . = {. + .: . ∈ ., . ∈ .}. If ., . are compact sets (i.e. bounded closed sets), then . is compact. In this case each of the sets ., ., . necessarily has a volume (its Lebesgue measure). Denote these volumes by .(.), .(.), .(.).

去才蔑視

Mixed Volumes,As before, . denotes the vector sum (Minkowski sum) of the subsets . and . of Euclidean space ?., while . = {.: . ∈ .} is the result of the homothety of . with coefficient .. In this chapter (except for Addendum 2), we consider only non-empty convex compact subsets of the space ?., often without saying it explicitly.

隨意

領帶

,Immersions in ?n,curvatures of (., .) with respect to the normal .., i.e. the eigenvalues of .(..). The vector.(the sum being taken over . from 1 to n ? m) does not depend on the choice of orthonormed basis {..} in .. This vector . is said to be the . of the .-dimensional surface (., .) at the point . ∈ . and its norm.is the ..

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