Calculus of Variations and Geometric Measure Theory

A. Goffi - F. Pediconi

A note on the strong maximum principle for fully nonlinear equations on Riemannian manifolds

created by goffi on 31 Jul 2020
modified on 29 Aug 2021


Published Paper

Inserted: 31 jul 2020
Last Updated: 29 aug 2021

Journal: The Journal of Geometric Analysis
Volume: 31
Number: 8
Pages: 8641-8665
Year: 2020
Doi: 10.1007/s12220-021-00607-2

ArXiv: 2007.15448 PDF


We investigate strong maximum (and minimum) principles for fully nonlinear second order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci's extremal operators, some singular operators like those modeled on the $p$- and $\infty$-Laplacian, and mean curvature type problems. As a byproduct, we establish new strong comparison principles for some second order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

Keywords: degenerate elliptic equation, Riemannian manifold, Fully nonlinear equation, Hopf boundary lemma, strong maximum principle, strong comparison principle