The Geometry of Total Curvature on Complete Open Surfaces


Author: Katsuhiro Shiohama,Shioya Tanaka,Takashi Shioya,Minoru Tanaka
Publisher: Cambridge University Press
ISBN: 9780521450546
Category: Mathematics
Page: 284
View: 1384
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This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.

Mean Curvature Flow and Isoperimetric Inequalities


Author: Manuel Ritoré,Carlo Sinestrari
Publisher: Springer Science & Business Media
ISBN: 3034602138
Category: Mathematics
Page: 114
View: 3119
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Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.

Geometric Control Theory and Sub-Riemannian Geometry


Author: Gianna Stefani,Ugo Boscain,Jean-Paul Gauthier,Andrey Sarychev,Mario Sigalotti
Publisher: Springer
ISBN: 331902132X
Category: Mathematics
Page: 384
View: 2599
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Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.

Linear and Projective Representations of Symmetric Groups


Author: Alexander Kleshchev,Kleshchev Alexander
Publisher: Cambridge University Press
ISBN: 9780521837033
Category: Mathematics
Page: 277
View: 2421
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Kleshchev describes a new approach to the subject of the representation theory of symmetric groups.

Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion


Author: Horst Osswald
Publisher: Cambridge University Press
ISBN: 1107016142
Category: Mathematics
Page: 407
View: 7796
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After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.

The Lévy Laplacian


Author: M. N. Feller
Publisher: Cambridge University Press
ISBN: 9781139447966
Category: Mathematics
Page: N.A
View: 6477
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The Lévy Laplacian is an infinite-dimensional generalization of the well-known classical Laplacian. The theory has become well developed in recent years and this book was the first systematic treatment of the Lévy–Laplace operator. The book describes the infinite-dimensional analogues of finite-dimensional results, and more especially those features which appear only in the generalized context. It develops a theory of operators generated by the Lévy Laplacian and the symmetrized Lévy Laplacian, as well as a theory of linear and nonlinear equations involving it. There are many problems leading to equations with Lévy Laplacians and to Lévy–Laplace operators, for example superconductivity theory, the theory of control systems, the Gauss random field theory, and the Yang–Mills equation. The book is complemented by an exhaustive bibliography. The result is a work that will be valued by those working in functional analysis, partial differential equations and probability theory.

Journal of the Mathematical Society of Japan


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 3604
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Mathematics of Computation


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 583
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American Book Publishing Record


Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 7184
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The British National Bibliography


Author: Arthur James Wells
Publisher: N.A
ISBN: N.A
Category: English literature
Page: N.A
View: 8542
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Forthcoming Books


Author: Rose Arny
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 1216
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Books in Print


Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Elementare Differentialgeometrie


Author: Christian Bär
Publisher: Walter de Gruyter
ISBN: 3110224593
Category: Mathematics
Page: 356
View: 9573
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This textbook presents an introduction to the differential geometry of curves and surfaces. This second, revised edition has been expanded to include solutions and applications in cartography. Topics include Euclidean geometry, curve theory, surface theory, curvature concepts, minimal surfaces, Riemann geometry and the Gauss-Bonnet theorem.

Geometrische Methoden in der Invariantentheorie


Author: Hanspeter Kraft
Publisher: Springer-Verlag
ISBN: 3663101436
Category: Technology & Engineering
Page: 308
View: 9065
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In dieser Einführung geht es vor allem um die geometrischen Aspekte der Invariantentheorie. Die hauptsächliche Motivation bildet das Studium von Klassifikations- und Normalformenproblemen, die auch historisch der Ausgangspunkt für invariantentheoretische Untersuchungen waren.

Lagerungen in der Ebene auf der Kugel und im Raum


Author: L. Fejes Toth
Publisher: Springer-Verlag
ISBN: 3662012065
Category: Mathematics
Page: 198
View: 2355
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Eine kurze Geschichte der Zeit


Author: Stephen Hawking
Publisher: Rowohlt Verlag GmbH
ISBN: 3644008612
Category: Science
Page: 272
View: 8298
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Ist das Universum unendlich oder begrenzt? Hat die Raumzeit einen Anfang, den Urknall? Dehnt sie sich aus? Wird sie wieder in sich zusammenstürzen? Liefe die Zeit dann rückwärts? Welchen Platz im Universum nehmen wir ein? Und ist in den atemberaubenden Modellen der Kosmologen noch Platz für einen Gott? – Es sind existenzielle Fragen, mit denen sich Stephen Hawking befasst, Fragen, die Forschung und Lehre in den Zentren der modernen Physik ebenso bestimmen wie die Diskussion von Geisteswissenschaftlern. Dieses Meisterwerk eines Jahrhundert-Genies hat unsere Weltsicht verändert. Zugleich hat Stephen Hawking damit neue Maßstäbe für die Erklärung komplexer physikalischer Zusammenhänge gesetzt. In diesem Buch, weltweit inzwischen über zehn Millionen Mal verkauft, ist das Credo des großen Physikers enthalten und lebendig. «Der Physiker Stephen Hawking ist im Begriff, die Formel zu finden, die das Universum erklärt.» ZEIT-Magazin

Equations Differentielles Operationnelles

Et Problèmes aux Limites
Author: Jacques Louis Lions
Publisher: Springer-Verlag
ISBN: 3662258390
Category: Mathematics
Page: 292
View: 2202
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Uniformisierung


Author: Rolf Nevanlinna
Publisher: Springer-Verlag
ISBN: 3642885616
Category: Mathematics
Page: 394
View: 9770
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Eine Vorlesung über Differentialgeometrie


Author: W. Klingenberg
Publisher: Springer-Verlag
ISBN: 3642655947
Category: Mathematics
Page: 138
View: 7843
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