幾何測度論(第4版)

幾何測度論(第4版)
定價：234 元
NT $ 204
 

內容簡介

This little book provides the newcomer or graduate student with’’an illustrated introduction to geometric measure theory: the basic ideas，terminology，and results.It developed from my one-semester course at MIT for graduate students with a semester of graduate real analysis behind them.I have included a few fundamental arguments and a superficial discussion of the regularity theory，but my goal is merely to introduce the subject and make the standard text.Geometric Measure Theory by H.Federer.more accessible.
 

目錄

Preface
1 Geometric Measure Theory
2 Measures
3 Lipschitz Functions and Rectifiable Sets
4 Normal and Rectifiable Currents
5 The Compactness Theorem and the Existence of Area-Minimizing Surfaces
6 Examples of Area-Minimizing Surfaces
7 The Approximation Theorem
8 Survey of Regularity Results
9 Monotonicity and Oriented Tangent Cones
10 The Regularity of Area-Minimizing Hypersurfaces
11 Flat Chains Modulo v Varifolds，and-Minimal Sets
12 Miscellaneous Useful Results
13 Soap Bubble Clusters
14 Proof of Double Bubble Conjecture
15 The Hexagonal Honeycomb and Kelvin Conjectures
16 Immiscible Fluids and Crystals
17 Isoperimetric Theorems in General Codimension
18 Manifolds with Density and Perelman’’s Proof of the Poincare Conjecture
19 Double Bubbles in Spheres，Gauss Space，and Tori
Solutions to Exercises
Bibliography
Index of Symbols
Name Index
Subject Index
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