Calculus on Manifolds

Calculus on Manifolds
Author: Michael Spivak
Publisher: Westview Press
Total Pages: 164
Release: 1965
Genre: Science
ISBN: 9780805390216

This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.

Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds

Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds
Author: Gerd Grubb
Publisher: American Mathematical Soc.
Total Pages: 338
Release: 2005
Genre: Mathematics
ISBN: 082183536X

In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.

Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds

Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds
Author: Raphael Ponge
Publisher: American Mathematical Soc.
Total Pages: 150
Release: 2008
Genre: Mathematics
ISBN: 0821841483

This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner andTaylor.

Advanced Real Analysis

Advanced Real Analysis
Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
Total Pages: 484
Release: 2008-07-11
Genre: Mathematics
ISBN: 0817644423

* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

Eigenfunctions of the Laplacian on a Riemannian Manifold

Eigenfunctions of the Laplacian on a Riemannian Manifold
Author: Steve Zelditch
Publisher: American Mathematical Soc.
Total Pages: 410
Release: 2017-12-12
Genre: Mathematics
ISBN: 1470410370

Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.

An Introduction to Manifolds

An Introduction to Manifolds
Author: Loring W. Tu
Publisher: Springer Science & Business Media
Total Pages: 426
Release: 2010-10-05
Genre: Mathematics
ISBN: 1441974008

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Analysis On Manifolds

Analysis On Manifolds
Author: James R. Munkres
Publisher: CRC Press
Total Pages: 296
Release: 2018-02-19
Genre: Mathematics
ISBN: 0429973772

A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.

Calculus on Heisenberg Manifolds

Calculus on Heisenberg Manifolds
Author: Richard Beals
Publisher: Princeton University Press
Total Pages: 212
Release: 1988-08-21
Genre: Business & Economics
ISBN: 9780691085012

The description for this book, Calculus on Heisenberg Manifolds. (AM-119), Volume 119, will be forthcoming.

Noncommutative Geometry and Global Analysis

Noncommutative Geometry and Global Analysis
Author: Henri Moscovici
Publisher: American Mathematical Soc.
Total Pages: 337
Release: 2011
Genre: Mathematics
ISBN: 0821849441

This volume represents the proceedings of the conference on Noncommutative Geometric Methods in Global Analysis, held in honor of Henri Moscovici, from June 29-July 4, 2009, in Bonn, Germany. Henri Moscovici has made a number of major contributions to noncommutative geometry, global analysis, and representation theory. This volume, which includes articles by some of the leading experts in these fields, provides a panoramic view of the interactions of noncommutative geometry with a variety of areas of mathematics. It focuses on geometry, analysis and topology of manifolds and singular spaces, index theory, group representation theory, connections of noncommutative geometry with number theory and arithmetic geometry, Hopf algebras and their cyclic cohomology.