The Kinematic Formula In Riemannian Homogeneous Spaces

Author : Ralph Howard
Publisher : American Mathematical Soc.
Page : 69 pages
File Size : 50,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825693

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The Kinematic Formula in Riemannian Homogeneous Spaces by Ralph Howard Pdf

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.

Author : D H Howard Howard
Publisher : Oxford University Press, USA
Page : 82 pages
File Size : 41,5 Mb
Release : 2014-08-31
Category : MATHEMATICS
ISBN : 1470400863

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Kinematic Formula in Riemannian Homogeneous Spaces by D H Howard Howard Pdf

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.

Author : Yongsheng Han,Eric T. Sawyer
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 41,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825921

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Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces by Yongsheng Han,Eric T. Sawyer Pdf

In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calder 'on reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.

Author : Wensheng Liu,Hector J. Sussmann
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 40,7 Mb
Release : 1995
Category : Extremal problems (Mathematics)
ISBN : 9780821804049

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Shortest Paths for Sub-Riemannian Metrics on Rank-Two Distributions by Wensheng Liu,Hector J. Sussmann Pdf

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.

Author : Alessandro Figà-Talamanca,Tim Steger
Publisher : American Mathematical Soc.
Page : 68 pages
File Size : 40,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825945

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Harmonic Analysis for Anisotropic Random Walks on Homogeneous Trees by Alessandro Figà-Talamanca,Tim Steger Pdf

This work presents a detailed study of the anisotropic series representations of the free product group $\mathbf Z/2\mathbf Z\star \cdots \star \mathbf Z/2\mathbf Z$. 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.

Author : Weiping Li,Shihshu Walter Wei
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 54,7 Mb
Release : 2015-08-25
Category : Geometry
ISBN : 9781470415563

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Geometry and Topology of Submanifolds and Currents by Weiping Li,Shihshu Walter Wei Pdf

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.

Author : Gregory S. Chirikjian
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 45,9 Mb
Release : 2011-11-15
Category : Mathematics
ISBN : 9780817649432

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Stochastic Models, Information Theory, and Lie Groups, Volume 2 by Gregory S. Chirikjian Pdf

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.

Author : Rainer Buckdahn
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 41,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825969

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Anticipative Girsanov Transformations and Skorohod Stochastic Differential Equations by Rainer Buckdahn Pdf

This book presents a survey of some recent developments in an important subfield of the new subject of anticipative stochastic analysis. D. Nualart and E. Pardoux have developed into a practicable calculus the theory of stochastic integration of processes not necessarily adapted to the driving Wiener process. This leads to anticipative stochastic differential equations with Skorohod integral and to anticipative Girsanov transformations, both of which are studied in the present work. The anticipative Girsanov transformations constitute the main tool for tackling stochastic differential equations with Skorohod integral. However, Buckdahn does not restrict attention only to this aspect but also considers different types of anticipative transformations and derives sufficient conditions for their absolute continuity with respect to the Wiener measure. The stochastic differential equations with Skorohod integral are studied under random initial conditions as well as under random boundary conditions.

Author : Takashi Shioya
Publisher : American Mathematical Soc.
Page : 73 pages
File Size : 47,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825785

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Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2-dimensional Riemannian Manifolds by Takashi Shioya Pdf

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.

Author : Semyon Alesker,Joseph H.G. Fu
Publisher : Springer
Page : 121 pages
File Size : 55,5 Mb
Release : 2014-10-09
Category : Mathematics
ISBN : 9783034808743

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Integral Geometry and Valuations by Semyon Alesker,Joseph H.G. Fu Pdf

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. ​

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814479974

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Contemporary Aspects of Complex Analysis, Differential Geometry and Mathematical Physics by Anonim Pdf

Author : F.J.E. Dillen,L.C.A. Verstraelen
Publisher : Elsevier
Page : 1067 pages
File Size : 41,5 Mb
Release : 1999-12-16
Category : Mathematics
ISBN : 9780080532837

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Handbook of Differential Geometry, Volume 1 by F.J.E. Dillen,L.C.A. Verstraelen Pdf

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.

Author : Ran Levi
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 49,9 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804018

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On Finite Groups and Homotopy Theory by Ran Levi Pdf

Let $p$ be a fixed prime number. Let $G$ denote a finite $p$-perfect group. This book looks at the homotopy type of the $p$-completed classifying space $BG_p$, where $G$ is a finite $p$-perfect group. The author constructs an algebraic analog of the Quillen's ``plus'' construction for differential graded coalgebras. This construction is used to show that given a finite $p$-perfect group $G$, the loop spaces $BG_p$ admits integral homology exponents. Levi gives examples to show that in some cases our bound is best possible. It is shown that in general $B\ast _p$ admits infinitely many non-trivial $k$-invariants. The author presents examples where homotopy exponents exist. Classical constructions in stable homotopy theory are used to show that the stable homotopy groups of these loop spaces also have exponents.

Author : A. L. Levin,Doron Shaul Lubinsky
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 52,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825990

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Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$ by A. L. Levin,Doron Shaul Lubinsky Pdf

Bounds for orthogonal polynomials which hold on the whole interval of orthogonality are crucial to investigating mean convergence of orthogonal expansions, weighted approximation theory, and the structure of weighted spaces. This book focuses on a method of obtaining such bounds for orthogonal polynomials (and their Christoffel functions) associated with weights on $[-1,1]$. Levin and Lubinsky obtain such bounds for weights that vanish strongly at 1 and $-1$. They also present uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.

Author : Huaxin Lin,Norman Christopher Phillips
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 55,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804032

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Classification of Direct Limits of Even Cuntz-Circle Algebras by Huaxin Lin,Norman Christopher Phillips Pdf

does not need NBB copy.