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Table of contents (16 chapters)
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Stochastic Lagrange Geometry
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Mean-Value Properties of Harmonic Functions
Keywords
About this book
The text proper begins with a brief introduction to stochastically derived Finslerian Laplacians, facilitated by applications in ecology, epidemiology and evolutionary biology. The mathematical ideas are then fully presented in section II, with generalizations to Lagrange geometry following in section III. With section IV, the focus abruptly shifts to the local mean-value approach to Finslerian Laplacians and a Hodge-de Rham theory is developed for the representation on real cohomology classes by harmonic forms on the base manifold. Similar results are proved in sections II and IV, each from different perspectives.
Modern topics treated include nonlinear Laplacians, Bochner and Lichnerowicz vanishing theorems, Weitzenböck formulas, and Finslerian spinors and Dirac operators. The tools developed in this book will find uses in several areas of physics and engineering, but especially in the mechanics of inhomogeneous media, e.g. Cofferat continua.
Audience: This text will be of use to workers in stochastic processes, differential geometry, nonlinear analysis, epidemiology, ecology and evolution, as well as physics of the solid state and continua.
Editors and Affiliations
Bibliographic Information
Book Title: The Theory of Finslerian Laplacians and Applications
Editors: Peter L. Antonelli, Bradley C. Lackey
Series Title: Mathematics and Its Applications
DOI: https://doi.org/10.1007/978-94-011-5282-2
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media Dordrecht 1998
Hardcover ISBN: 978-0-7923-5313-3Published: 31 October 1998
Softcover ISBN: 978-94-010-6223-7Published: 10 October 2012
eBook ISBN: 978-94-011-5282-2Published: 06 December 2012
Edition Number: 1
Number of Pages: XXX, 282
Topics: Number Theory, Global Analysis and Analysis on Manifolds, Probability Theory and Stochastic Processes, Mathematical Modeling and Industrial Mathematics, Differential Geometry, Evolutionary Biology