## ＜電子ブック＞Stability Theorems in Geometry and Analysis

責任表示 by Yu. G. Reshetnyak Reshetnyak, Yu. G SpringerLink (Online service) English (英語) Springer Netherlands Imprint: Springer 1994- Dordrecht, Netherlands シリーズ Mathematics and Its Applications ; 304 1. Preliminaries, Notation, and Terminology n n 1.1. Sets and functions in lR. - Throughout the book, lR. stands for the n-dimensional arithmetic space of points x = (X},X2,'" ,xn)j Ixl is the length ...of n n a vector x E lR. and (x, y) is the scalar product of vectors x and y in lR. , i.e., for x = (Xl, X2, -.- , xn) and y = (y}, Y2,··., Yn), Ixl = Jx~ + x~ + ... + x~, (x, y) = XIYl + X2Y2 + ... + XnYn. n Given arbitrary points a and b in lR. , we denote by [a, b] the segment that joins n them, i.e. the collection of points x E lR. of the form x = >.a + I'b, where>. + I' = 1 and >. ~ 0, I' ~ O. n We denote by ei, i = 1,2, ... ,n, the vector in lR. whose ith coordinate is equal to 1 and the others vanish. The vectors el, e2, ... ,en form a basis for the space n lR. , which is called canonical. If P( x) is some proposition in a variable x and A is a set, then {x E A I P(x)} denotes the collection of all the elements of A for which the proposition P( x) is true.続きを見る 1. Introduction2. Möbius Transformations3. Integral Representations and Estimates for Differentiable Functions4. Stability in Liouville's Theorem on Conformal Mappings in Space5. Stability of Isometric Transformations of the Space ?n6. Stability in Darboux's Theorem7. Differential Properties of Mappings with Bounded Distortion and Conformal Mappings of Riemannian SpacesReferences. Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive)

### 詳細

レコードID 3641505 QA307 QA432 515.72 Mathematics. Topological Groups. Integral equations. Integral Transforms. Geometry. Mathematical optimization. Mathematics. Integral Transforms, Operational Calculus. Integral Equations. Geometry. Calculus of Variations and Optimal Control; Optimization. Topological Groups, Lie Groups. ssj0001298526 9789048144679(print) 9789401583602 2020.06.27 2020.06.28