Liouville theorems for semilinear differential inequalities on sub-Riemannian manifolds

Differential Inequalities on Complete Riemannian Manifolds and Applications

This paper treats various aspects of the asymptotic behavior of solutions of certain elliptic equations of geometric interest on complete Riemannian manifolds. Sharp results relating the rate of volume growth of a complete Riemannian manifold and the growth of its harmonic and subharmonic functions can be found in E22] together with references to related results. In Sect. 2 of this paper we con...

Differential Harnack Inequalities on Riemannian Manifolds I : Linear Heat Equation

Abstract. In the first part of this paper, we get new Li-Yau type gradient estimates for positive solutions of heat equation on Riemmannian manifolds with Ricci(M) ≥ −k, k ∈ R. As applications, several parabolic Harnack inequalities are obtained and they lead to new estimates on heat kernels of manifolds with Ricci curvature bounded from below. In the second part, we establish a Perelman type L...

Liouville type theorems and Harnack type inequalities for semilinear elliptic equations

Quasilinear elliptic inequalities on complete Riemannian manifolds

We prove maximum and comparison principles for weak distributional solutions of quasilinear, possibly singular or degenerate, elliptic differential inequalities in divergence form on complete Riemannian manifolds. A new definition of ellipticity for nonlinear operators on Riemannian manifolds is introduced, covering the standard important examples. As an application, uniqueness results for some...

On Sublaplacians of Sub-riemannian Manifolds

In this note we address a notion of sublaplacians of sub-Riemannian manifolds. In particular for fat sub-Riemannian manifolds we answered the sublaplacian question proposed by R. Montgomery in [21, p.142]