The divergence theorem and the Laplacian in Minkowski space
type: Item
instance of: scholarly article
title: The divergence theorem and the Laplacian in Minkowski space
zbMATH Open document ID: 0877.52006
DOI: 10.1007/BF00148216
author: Yanyan Li
published in: Geometriae Dedicata
publication date: 1996-11-07T00:00:00Z
review text: Given a Minkowski space (a finite-dimensional Banach space), the authors define a Minkowskian notion of divergence for 1-forms and prove a corresponding divergence theorem. Since the Euclidean divergence theorem involves unit normal vectors and area integration, for the Minkowski counterpart one needs not only Minkowskian length and a notion of normality (here Birkhoff's definition is used), but also a Minkowskian notion of surface area. This can here be any Minkowskian area satisfying the usual axioms and specified by a convex isoperimetrix. After establishing the divergence for 1-forms, the authors define a Minkowskian Laplace operator by applying the divergence to the differential of a function. It is proved that this Laplacian is a second-order, constant-coefficient, elliptic differential operator. Its symbol is computed and used to assign a natural Euclidean structure with the Minkowski space.
reviewed by: Rolf Schneider
Mathematics Subject Classification ID: 52A21
zbMATH DE Number: 942746
zbMATH Keywords: elliptic operator
zbMATH Keywords: ellipsoid
zbMATH Keywords: Minkowski space
zbMATH Keywords: divergence
zbMATH Keywords: Laplacian
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00148216
OpenAlex ID: W2013809867
description: scientific article; zbMATH DE number 942746