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The Theory of Finslerian Laplacians and Applications

  • Peter L. Antonelli
  • Bradley C. Lackey
Book

Part of the Mathematics and Its Applications book series (MAIA, volume 459)

Table of contents

  1. Front Matter
    Pages i-xxx
  2. Finsler Laplacians in Application

    1. P. L. Antonelli, T. J. Zastawniak
      Pages 1-12
    2. P. L. Antonelli, T. J. Zastawniak
      Pages 33-46
  3. Stochastic Analysis and Brownian Motion

    1. P. L. Antonelli, T. J. Zastawniak
      Pages 47-62
    2. P. L. Antonelli, T. J. Zastawniak
      Pages 63-88
    3. P. L. Antonelli, T. J. Zastawniak
      Pages 89-110
  4. Stochastic Lagrange Geometry

    1. Dragoş Hrimiuc
      Pages 111-121
    2. P. L. Antonelli, D. Hrimiuc
      Pages 123-131
    3. P. L. Antonelli, D. Hrimiuc
      Pages 133-139
  5. Mean-Value Properties of Harmonic Functions

    1. P. L. Antonelli, T. J. Zastawniak
      Pages 141-149
    2. Paul Centore
      Pages 151-186
  6. Analytical Constructions

About this book

Introduction

Finslerian Laplacians have arisen from the demands of modelling the modern world. However, the roots of the Laplacian concept can be traced back to the sixteenth century. Its phylogeny and history are presented in the Prologue of this volume.
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.

Keywords

Evolution Operator calculus differential equation evolutionary biology geometry mechanics modeling phylogeny theory of evolution

Editors and affiliations

  • Peter L. Antonelli
    • 1
  • Bradley C. Lackey
    • 1
  1. 1.Department of Mathematical SciencesUniversity of AlbertaEdmontonCanada

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