A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry

Andersson, L.; Galloway, G. J.; Howard, R.

A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry

Authors

Andersson, L.

Galloway, G. J.

Howard, R.

Description

The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for $C^0$ spacelike hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped product splitting theorem is given.
37 pages, 1 figure, ams-latex using eepic