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Stability Theorems in Geometry and Analysis

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概要 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
目次 1. Introduction
2. Möbius Transformations
3. Integral Representations and Estimates for Differentiable Functions
4. Stability in Liouville's Theorem on Conformal Mappings in Space
5. Stability of Isometric Transformations of the Space ?n
6. Stability in Darboux's Theorem
7. Differential Properties of Mappings with Bounded Distortion and Conformal Mappings of Riemannian Spaces
References.
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登録日 2020.06.27
更新日 2020.06.28