Stability Theorems in Geometry and Analysis: 304 - Rilegato

Reshetnyak, Yu. G.

Rilegato

ISBN 10: 0792331184 ISBN 13: 9780792331186

Casa editrice: Kluwer Academic Pub, 1994

Riassunto

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.

Su questo libro

Contenuti:

Foreword to the English Translation. Preface to the First Russian Edition. 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 Rn. 6. Stability in Darboux's Theorem. 7. Differential Properties of Mappings with Bounded Distortion and Conformal Mappings of Riemannian Spaces. References. Subject Index.

Product Description:

Book by Reshetnyak YuG

Su questa edizione

• Editore: Kluwer Academic Pub
• Data di pubblicazione: 1994
• ISBN 10: 0792331184
• ISBN 13: 9780792331186
• Rilegatura: Copertina rigida
• Numero di pagine: 412