Geometric Measure Theory, Fourth Edition, is an excellent text for introducing ideas from geometric measure theory and the calculus of variations to beginning graduate students and researchers. This updated edition contains abundant illustrations, examples, exercises, and solutions; and the latest results on soap bubble clusters, including a new chapter on Double Bubbles in Spheres, Gauss Space, and Tori. It also includes a new chapter on Manifolds with Density and Perelman's Proof of the Poincaré Conjecture. This text is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject. New to the 4th edition: * Abundant illustrations, examples, exercises, and solutions. * The latest results on soap bubble clusters, including a new chapter on "Double Bubbles in Spheres, Gauss Space, and Tori." * A new chapter on "Manifolds with Density and Perelman's Proof of the Poincaré Conjecture." * Contributions by undergraduates.
Facts101 is your complete guide to Geometric Measure Theory, A Beginners Guide. In this book, you will learn topics such as Normal and Rectifiable Currents, The Compactness Theorem and the Existence of Area-Minimizing Surfaces, Examples of Area-Minimizing Surfaces, and The Approximation Theorem plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.
Der Band enthält zehn mathematische oder mathematikhistorische Beiträge, die in exemplarischer Weise Bedeutung und Wirkung wichtiger Arbeiten von Hausdorff darstellen. Darunter sind Beiträge von Mathematikern aller drei Universitäten, an denen Hausdorff gelehrt hat: Leipzig, Greifswald und Bonn. Der Gedenkband "Felix Hausdorff zum Gedächtnis" erschien aus Anlass von Hausdorffs 50. Todestag. Er erinnert an das Werk, das Leben und das Schicksal dieses bedeutenden Mathematikers in der Zeit der nationalsozialistischen Verfolgung der Juden.
This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in Mn, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions). Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.
This new series offers the most comprehensive views of key areas in the world of science. Each set explores all facets of the topic, offering not only descriptive and analytical information, but also cultural and ethical issues, and career opportunities in many fields of science.
Der Integralbegriff in seiner Ausprägung durch Henri Lebesgue ist ein grundlegendes Werkzeug in der modernen Analysis, Numerik und Stochastik. Für Lehrveranstaltungen zu diesen Gebieten der Mathematik bereiten die Autoren wesentliche Sachverhalte in kompakter Weise auf. Das Buch liefert Orientierung und Material für verschiedene Varianten zwei- oder vierstündiger Lehrveranstaltungen. In einem ergänzenden Abschnitt werden um den Begriff der Konvexität herum Verbünde zur Funktionalanalysis hergestellt.