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

1997/07/22 by Lars Andersson, Andersson, L., Gregory J. Galloway +3 · 1 citation
Mathematics · #35B50 (Primary) 53C21 #58G03 #83C75 (Secondary) #Advanced Mathematical Physics Problems #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.dg-ga/9707015

openalex publication_date 1997/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 C⁰ spacelike hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped product splitting theorem is given.

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