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Moduli Spaces of Riemannian Metrics
This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.
Differential Geometry in the Large
From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.
Geometric Relativity
Many problems in general relativity are essentially geometric in nature, in the sense that they can be understood in terms of Riemannian geometry and partial differential equations. This book is centered around the study of mass in general relativity using the techniques of geometric analysis. Specifically, it provides a comprehensive treatment of the positive mass theorem and closely related results, such as the Penrose inequality, drawing on a variety of tools used in this area of research, including minimal hypersurfaces, conformal geometry, inverse mean curvature flow, conformal flow, spinors and the Dirac operator, marginally outer trapped surfaces, and density theorems. This is the fir...
Alpine Perspectives on Algebraic Topology
Contains the proceedings of the Third Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, on August 18-24, 2008. This title includes research papers on stable homotopy theory, the theory of operads, localization and algebraic K-theory, as well as survey papers on the Witten genus and localization techniques.
Faltpuzzles Selbstportraits
Die Faltpuzzles von Klaus Schröer sind einfach ein Stück Papier mit einem deckungsgleichen Faltraster auf beiden Seiten, das die Puzzleteile enthält. Die Regeln sind simpel: Falten Sie das Papier unter ausschließlicher Nutzung der Linien des Faltrasters, bis Sie das Zielmotiv zusammengefaltet haben. 44 Seiten, 16 farbige Faltpuzzles zum Ausschneiden, Deutsch / Englisch (der Buchblock wird im internationalen Vertrieb in Graustufen gedruckt) The folding puzzles by Klaus Schröer are just a simple piece of paper with a folding grid congruent on both sides containing the tiles of the puzzle. The rules are simple: Just fold the paper using only the lines of the grid until you reached the target image. 44 pages, 16 colored folding puzzles to cut out, German / English (the book block is printed in grayscale in international sales)
Postmodern Analysis
What is the title of this book intended to signify, what connotations is the adjective "Postmodern" meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the approach to analysis presented here from what has been called "Modern Analysis" by its protagonists. "Modern Analysis" as represented in the works of the Bour baki group or in the textbooks by Jean Dieudonne is characterized by its systematic and axiomatic treatment and by its drive towards a high level of abstraction. Given the tendency of many prior treatises on analysis to degen erate into a collection of rather unconnected tricks to solve special problems, this definite...
Riemannian Geometry and Geometric Analysis
The present textbook is a somewhat expanded version of the material of a three-semester course I gave in Bochum. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds. In the first chapter, we introduce the basic geometric concepts, like dif ferentiable manifolds, tangent spaces, vector bundles, vector fields and one parameter groups of diffeomorphisms, Lie algebras and groups and in par ticular Riemannian metrics. We also derive some elementary results about geodesics. The second chapter introduces de Rham cohomology groups and the es sential tools from elliptic PDE for treating these groups. In later chapters, we shall encounter nonlinear versions o...
Differential Geometry - Proceedings Of The Viii International Colloquium
This volume contains research and expository papers on recent advances in foliations and Riemannian geometry. Some of the topics covered in this volume include: topology, geometry, dynamics and analysis of foliations, curvature, submanifold theory, Lie groups and harmonic maps.Among the contributions, readers may find an extensive survey on characteristic classes of Riemannian foliations offering also new results, an article showing the uniform simplicity of certain diffeomorphism groups, an exposition of convergences of contact structures to foliations from the point of view of Thurston's and Thurston-Bennequin's inequalities, a discussion about Fatou-Julia decompositions for foliations and...
An Invitation to Alexandrov Geometry
Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.
A Panoramic View of Riemannian Geometry
This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS
