The Kinematic Formula In Riemannian Homogeneous Spaces

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The Kinematic Formula In Riemannian Homogeneous Spaces

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Author : Ralph Howard
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

The Kinematic Formula In Riemannian Homogeneous Spaces written by Ralph Howard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

This memoir investigates a method that generalizes the Chern-Federer kinematic formula to arbitrary homogeneous spaces with an invariant Riemannian metric, and leads to new formulas even in the case of submanifolds of Euclidean space.

Kinematic Formula In Riemannian Homogeneous Spaces

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Author : D H Howard Howard
language : en
Publisher: Oxford University Press, USA
Release Date : 2014-08-31

Kinematic Formula In Riemannian Homogeneous Spaces written by D H Howard Howard and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-31 with MATHEMATICS categories.

This book shows that much of classical integral geometry can be derived from the coarea formula by some elementary techniques. Howard generalizes much of classical integral geometry from spaces of constant sectional curvature to arbitrary Riemannian homogeneous spaces. To do so, he provides a general definition of an integral invariant'' of a submanifold of the space that is sufficiently general enough to cover most cases that arise in integral geometry. Working in this generality makes it clear that the type of integral geometric formulas that hold in a space does not depend on the full group of isometries, but only on the isotropy subgroup. As a special case, integral geometric formulas that hold in Euclidean space also hold in all the simply connected spaces of constant curvature. Detailed proofs of the results and many examples are included. Requiring background of a one-term course in Riemannian geometry, this book may be used as a textbook in graduate courses on differential and integral geometry.

Shortest Paths For Sub Riemannian Metrics On Rank Two Distributions

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Author : Wensheng Liu
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

Shortest Paths For Sub Riemannian Metrics On Rank Two Distributions written by Wensheng Liu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

A sub-Riemannian manifold ([italic capitals]M, E, G) consists of a finite-dimensional manifold [italic capital]M, a rank-two bracket generating distribution [italic capital]E on [italic capital]M, and a Riemannian metric [italic capital]G on [italic capital]E. All length-minimizing arcs on ([italic capitals]M, E, G) are either normal extremals or abnormal extremals. Normal extremals are locally optimal, i.e., every sufficiently short piece of such an extremal is a minimizer. The question whether every length-minimizer is a normal extremal was recently settled by R. G. Montgomery, who exhibited a counterexample. The present work proves that regular abnormal extremals are locally optimal, and, in the case that [italic capital]E satisfies a mild additional restriction, the abnormal minimizers are ubiquitous rather than exceptional. All the topics of this research report (historical notes, examples, abnormal extremals, Hamiltonians, nonholonomic distributions, sub-Riemannian distance, the relations between minimality and extremality, regular abnormal extremals, local optimality of regular abnormal extremals, etc.) are presented in a very clear and effective way.

Harmonic Analysis For Anisotropic Random Walks On Homogeneous Trees

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Author : Alessandro Figà-Talamanca
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Harmonic Analysis For Anisotropic Random Walks On Homogeneous Trees written by Alessandro Figà-Talamanca and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This work presents a detailed study of the anisotropic series representations of the free product group Z/2Z*...*Z/2Z. These representations are infinite dimensional, irreducible, and unitary and can be divided into principal and complementary series. Anisotropic series representations are interesting because, while they are not restricted from any larger continuous group in which the discrete group is a lattice, they nonetheless share many properties of such restrictions. The results of this work are also valid for nonabelian free groups on finitely many generators.

Stochastic Models Information Theory And Lie Groups Volume 2

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Author : Gregory S. Chirikjian
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-15

Stochastic Models Information Theory And Lie Groups Volume 2 written by Gregory S. Chirikjian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-15 with Mathematics categories.

This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

Anticipative Girsanov Transformations And Skorohod Stochastic Differential Equations

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Author : Rainer Buckdahn
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Anticipative Girsanov Transformations And Skorohod Stochastic Differential Equations written by Rainer Buckdahn and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This monograph presents a concise exposition of recent developments in anticipative stochastic calculus. The anticipative calculus uses tools from differential calculus and distribution theory on Wiener space to analyze stochastic integrals with integrands which can anticipate the future of the Brownian integrator. In particular, the Skorohod integral, defined as a dual operator to the Wiener space derivative, and the anticipating Stratonovich integrals are fundamental.

Behavior Of Distant Maximal Geodesics In Finitely Connected Complete 2 Dimensional Riemannian Manifolds

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Author : Takashi Shioya
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Behavior Of Distant Maximal Geodesics In Finitely Connected Complete 2 Dimensional Riemannian Manifolds written by Takashi Shioya and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many illustrations that enhance understanding of the main ideas.

Integral Geometry And Valuations

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Author : Semyon Alesker
language : en
Publisher: Springer
Release Date : 2014-10-09

Integral Geometry And Valuations written by Semyon Alesker and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-09 with Mathematics categories.

In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, provides an introduction to the theory of convex valuations with emphasis on recent developments. In particular, it presents the new structures on the space of valuations discovered after Alesker's irreducibility theorem. The newly developed theory of valuations on manifolds is also described. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló. The approach is new and based on the notions and tools presented in the first part. This original viewpoint not only enlightens the classical integral geometry of euclidean space, but it also allows the computation of kinematic formulas in other geometries, such as hermitian spaces. The book will appeal to graduate students and interested researchers from related fields including convex, stochastic, and differential geometry. ​

Geometry And Topology Of Submanifolds And Currents

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Author : Weiping Li
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-08-25

Geometry And Topology Of Submanifolds And Currents written by Weiping Li and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-25 with Mathematics categories.

he papers in this volume are mainly from the 2013 Midwest Geometry Conference, held October 19, 2013, at Oklahoma State University, Stillwater, OK, and partly from the 2012 Midwest Geometry Conference, held May 12-13, 2012, at the University of Oklahoma, Norman, OK. The papers cover recent results on geometry and topology of submanifolds. On the topology side, topics include Plateau problems, Voevodsky's motivic cohomology, Reidemeister zeta function and systolic inequality, and freedom in 2- and 3-dimensional manifolds. On the geometry side, the authors discuss classifying isoparametric hypersurfaces and review Hartogs triangle, finite volume flows, nonexistence of stable p-currents, and a generalized Bernstein type problem. The authors also show that the interaction between topology and geometry is a key to deeply understanding topological invariants and the geometric problems.

Handbook Of Differential Geometry Volume 1

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Author : F.J.E. Dillen
language : en
Publisher: Elsevier
Release Date : 1999-12-16

Handbook Of Differential Geometry Volume 1 written by F.J.E. Dillen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-16 with Mathematics categories.

In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.