Stability Theorems in Geometry and Analysis

1994
ISBN: 978-0-7923-3118-6
Verlag: Springer Netherlands

Buch, Englisch, Band 304, 394 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1660 g

Reihe: Mathematics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Reshetnyak, Yu. G.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis

Inhaltsverzeichnis

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.