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,
WeitzenbAck 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.
General
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