Metric Structures for Riemannian and Non-Riemannian Spaces

Metric Structures for Riemannian and Non-Riemannian Spaces PDF Author: Mikhail Gromov
Publisher: Springer Science & Business Media
ISBN: 0817645837
Category : Mathematics
Languages : en
Pages : 594

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Book Description
This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.

Metric Structures for Riemannian and Non-Riemannian Spaces

Metric Structures for Riemannian and Non-Riemannian Spaces PDF Author: Mikhail Gromov
Publisher: Springer Science & Business Media
ISBN: 0817645837
Category : Mathematics
Languages : en
Pages : 594

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Book Description
This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.

Metric Structures for Riemannian and Non-Riemannian Spaces

Metric Structures for Riemannian and Non-Riemannian Spaces PDF Author: Mikhael Gromov
Publisher:
ISBN:
Category : Riemannian manifolds
Languages : en
Pages : 585

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Book Description


Metric Structures for Riemannian and Non-Riemannian Spaces

Metric Structures for Riemannian and Non-Riemannian Spaces PDF Author: Mikhail Gromov
Publisher: Birkhäuser
ISBN: 9780817671440
Category : Mathematics
Languages : en
Pages : 586

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Book Description
This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.

Introduction To Modern Finsler Geometry

Introduction To Modern Finsler Geometry PDF Author: Yi-bing Shen
Publisher: World Scientific Publishing Company
ISBN: 981470492X
Category : Mathematics
Languages : en
Pages : 406

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Book Description
This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.

Mathematics Going Forward

Mathematics Going Forward PDF Author: Jean-Michel Morel
Publisher: Springer Nature
ISBN: 3031122445
Category : Mathematics
Languages : en
Pages : 629

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Book Description
This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.

Some Novel Types of Fractal Geometry

Some Novel Types of Fractal Geometry PDF Author: Stephen Semmes
Publisher: Oxford University Press
ISBN: 9780198508069
Category : Mathematics
Languages : en
Pages : 180

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Book Description
This book deals with fractal geometries that have features similar to ones of ordinary Euclidean spaces, while at the same time being quite different from Euclidean spaces.. A basic example of this feature considered is the presence of Sobolev or Poincaré inequalities, concerning the relationship between the average behavior of a function and the average behavior of its small-scale oscillations. Remarkable results in the last few years through Bourdon-Pajot and Laakso have shown that there is much more in the way of geometries like this than have been realized, only examples related to nilpotent Lie groups and Carnot metrics were known previously. On the other had, 'typical' fractals that might be seen in pictures do not have these same kinds of features. This text examines these topics in detail and will interest graduate students as well as researchers in mathematics and various aspects of geometry and analysis.

Geometric Possibility

Geometric Possibility PDF Author: Gordon Belot
Publisher: Oxford University Press, USA
ISBN: 0199595321
Category : Philosophy
Languages : en
Pages : 230

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Book Description
Relationalism seeks to ground all claims about the structure of space in facts about actual and possible configurations of matter. Gordon Belot elucidates the prospects for this view of the nature of space by investigating the kew notion of geometric possibility in relation to philosophical notions of physical possibility.

Real and Complex Submanifolds

Real and Complex Submanifolds PDF Author: Young Jin Suh
Publisher: Springer
ISBN: 4431552154
Category : Mathematics
Languages : en
Pages : 510

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Book Description
Edited in collaboration with the Grassmann Research Group, this book contains many important articles delivered at the ICM 2014 Satellite Conference and the 18th International Workshop on Real and Complex Submanifolds, which was held at the National Institute for Mathematical Sciences, Daejeon, Republic of Korea, August 10–12, 2014. The book covers various aspects of differential geometry focused on submanifolds, symmetric spaces, Riemannian and Lorentzian manifolds, and Kähler and Grassmann manifolds.

Surveys in Geometry I

Surveys in Geometry I PDF Author: Athanase Papadopoulos
Publisher: Springer Nature
ISBN: 3030866955
Category : Mathematics
Languages : en
Pages : 469

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Book Description
The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner. The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (Bishop—Gromov type inequalities in Gromov-hyperbolic spaces), convexity theory and inequalities involving volumes and mixed volumes of convex bodies, 4-dimensional topology, Teichmüller spaces and mapping class groups actions, translation surfaces and their dynamics, and complex higher-dimensional geometry. Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to current research trends in geometry.

Spectral Analysis on Graph-like Spaces

Spectral Analysis on Graph-like Spaces PDF Author: Olaf Post
Publisher: Springer
ISBN: 3642238408
Category : Mathematics
Languages : en
Pages : 444

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Book Description
Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm convergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abstract definition of resonances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.