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Metric Structures For Riemannian And Non Riemannian Spaces

Author: Mikhail Gromov
Publisher: Springer Science & Business Media
ISBN: 0817645837
Size: 54.40 MB
Format: PDF, ePub
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This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.

Function Spaces And Partial Differential Equations

Author: Ali Taheri
Publisher: Oxford University Press, USA
ISBN: 0198733135
Size: 72.34 MB
Format: PDF, Mobi
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This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Modern Approaches To Discrete Curvature

Author: Laurent Najman
Publisher: Springer
ISBN: 3319580027
Size: 24.84 MB
Format: PDF, Docs
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This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.

Function Spaces And Partial Differential Equations

Author: Ali Taheri
Publisher: Oxford University Press, USA
ISBN: 0198733151
Size: 41.91 MB
Format: PDF, Docs
View: 5032
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This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Bernhard Riemann 1826 1866

Author: Detlef Laugwitz
Publisher: Springer-Verlag
ISBN: 3034889836
Size: 33.49 MB
Format: PDF
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Das Riemannsche Integral lernen schon die Schüler kennen, die Theorien der reellen und der komplexen Funktionen bauen auf wichtigen Begriffsbildungen und Sätzen Riemanns auf, die Riemannsche Geometrie ist für Einsteins Gravitationstheorie und ihre Erweiterungen unentbehrlich, und in der Zahlentheorie ist die berühmte Riemannsche Vermutung noch immer offen. Riemann und sein um fünf Jahre jüngerer Freund Richard Dedekind sahen sich als Schüler von Gauss und Dirichlet. Um die Mitte des 19. Jahrhunderts leiteten sie den Übergang zur "modernen Mathematik" ein, der eine in Analysis und Geometrie, der andere in der Algebra mit der Hinwendung zu Mengen und Strukturen. Dieses Buch ist der erste Versuch, Riemanns wissenschaftliches Werk unter einem einheitlichen Gesichtspunkt zusammenzufassend darzustellen. Riemann gilt als einer der Philosophen unter den Mathematikern. Er stellte das Denken in Begriffen neben die zuvor vorherrschende algorithmische Auffassung von der Mathematik, welche die Gegenstände der Untersuchung, in Formeln und Figuren, in Termumformungen und regelhaften Konstruktionen als die allein legitimen Methoden sah. David Hilbert hat als Riemanns Grundsatz herausgestellt, die Beweise nicht durch Rechnung, sondern lediglich durch Gedanken zu zwingen. Hermann Weyl sah als das Prinzip Riemanns in Mathematik und Physik, "die Welt als das erkenntnistheoretische Motiv..., die Welt aus ihrem Verhalten im un- endlich kleinen zu verstehen."