《幾何測度論》是2009年世界圖書出版公司出版的圖書，作者是（美國）摩根 (Morgan.F.)。
基本介紹
- 中文名：幾何測度論
- 作者：摩根
- 出版社：世界圖書出版公司
- 出版時間：2009年5月
- 頁數：248 頁
- 定價：39.00 元
- 開本：16 開
- 裝幀：平裝
- ISBN：9787506292085
內容簡介,目錄,
內容簡介
《幾何測度論(第4版)》是摩根編著的，Singular geometry governs the physical universe: soap bubble clusters meeting along singular curves, black holes, defects in materials, chaotic turbulence, crys- tal growth. The governing principle is often some kind of energy minimization. Geometric measure theory provides a general framework for understanding such minimal shapes, a priori allowing any imaginable singularity and then proving that only certain kinds of structures occur.
目錄
Preface vii
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
Suhiect Index
