The Divergence Theorem and the Laplacian in Minkowski Space

Authors: Thompson A.A.¹; Thompson A.C.²

Source: Geometriae Dedicata, Volume 63, Number 2, November 1996 , pp. 159-170(12)

Publisher: Springer

Abstract:

Let (X,B) be a Minkowski space (finite-dimensional Banach space) with unit ball B. Using a Minkowski definition of unit normal to a hypersurface, a Minkowski analogue of Euclidean divergence is defined. We show that the divergence theorem holds. Using the Minkowski divergence, a Minkowski Laplacian is defined. We prove that this Laplacian is a second-order, constant-coefficient, elliptic, differential operator. Furthermore, the symbol of this Laplacian is computed and used to associate a natural Euclidean structure with (X,B).

Keywords: Minkowski space; divergence; Laplacian; elliptic operator; ellipsoid

Language: English

Document Type: Regular paper

Affiliations: 1: Array Systems Computing, 401 Magnetic Drive, Suite 24, Downsview, Ontario, Canada M3J 3H9. e-mail: alan@array.ca 2: Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5. e-mail: tony@cs.dal.ca

Publication date: 1996-11-01

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• By this author: Thompson A.A. ;  Thompson A.C.

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