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Stability Theorems in Geometry and Analysis: 304 (Mathematics and Its Applications, 304) - Tapa dura

Reshetnyak, Yu.G.

 
9780792331186: Stability Theorems in Geometry and Analysis: 304 (Mathematics and Its Applications, 304)
Tapa dura
ISBN 10: 0792331184 ISBN 13: 9780792331186
Editorial: Springer, 1994

Sinopsis

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.

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Reseña del editor

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.

Reseña del editor

This is one of the first monographs to deal with the metric theory of spatial mappings and incorporates results in the theory of quasi-conformal, quasi-isometric and other mappings.
The main subject is the study of the stability problem in Liouville's theorem on conformal mappings in space, which is representative of a number of problems on stability for transformation classes. To enable this investigation a wide range of mathematical tools has been developed which incorporate the calculus of variation, estimates for differential operators like Korn inequalities, properties of functions with bounded mean oscillation, etc.
Results obtained by others researching similar topics are mentioned, and a survey is given of publications treating relevant questions or involving the technique proposed.
This volume will be of great value to graduate students and researchers interested in geometric function theory.

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Editorial
Springer
Año de publicación
1994
Idioma
Inglés
ISBN 10 
0792331184
ISBN 13 
9780792331186
Encuadernación
Tapa dura
Número de páginas
412
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