Geometric measure theory : a beginner's guide
著者
書誌事項
Geometric measure theory : a beginner's guide
Academic Press, c1995
2nd ed
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注記
Bibliography: p. 157-164
Includes indexes
内容説明・目次
内容説明
Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Morgan emphasizes geometry over proofs and technicalities, and includes a bibliography and abundant illustrations and examples. This Second Edition features a new chapter on soap bubbles as well as updated sections addressing volume constraints, surfaces in manifolds, free boundaries, and Besicovitch constant results. The text will introduce newcomers to the field and appeal to mathematicians working in the field.
目次
Preface. Geometric Measure Theory. Measures. Lipschitz Functions and Rectifiable Sets. Normal and Rectifiable Currents. The Compactness Theorem and the Existence of Area-Minimizing Surfaces. Examples of Area-Minimizing Surfaces. The Approximation Theorem. Survey of Regularity Results. Monotonicity and Oriented Tangent Cones. The Regularity of Area-Minimizing Hypersurfaces. Flat Chains Modulo (, Varifolds, and (M, (, ()-Minimal Sets. Miscellaneous Useful Results. Soap Bubble Clusters. Solutions to Exercises. Bibliography. Index of Symbols. Author Index. Subject Index.
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