Harnack inequality for quasilinear elliptic equations on Riemannian manifolds (Q1678234)

This paper concerns viscosity solutions to degenerate and singular elliptic equations \[ {\mathcal L}_F [u] := \operatorname{div} \bigg(\frac{F'(|\nabla u|)}{|\nabla u|} \nabla u \bigg) = h \] of \(p\)-Laplacian type on a complete Riemannian manifold \(M\), provided that an even function \(F \in C^1 (\mathbb{R})\cap C^2 (0,\infty)\) is strictly convex on \((0,\infty)\) and satisfies either \(F\in C^2(\mathbb{R})\) or its convex conjugate \(F^\ast\in C^2(\mathbb{R})\) with some growth condition. In this paper, the author proves a (locally) uniform Aleksandrov-Bakelman-Pucci type estimate and a Krylov-Safonov type Harnack estimate for such kind of solutions using a geometrical approach.