On the maximum principle for principal curvatures

Principal Curvatures of Surfaces

Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators

We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, the maximum principle refers to the property of non-positivity of viscosity subsolutions of the Dirichlet problem. The new notion of generalized principal eigenvalue that we introduce here al...

Principal curvatures from the integral invariant viewpoint

The extraction of curvature information for surfaces is a basic problem of Geometry Processing. Recently an integral invariant solution of this problem was presented, which is based on principal component analysis of local neighbourhoods defined by kernel balls of various sizes. It is not only robust to noise, but also adjusts to the level of detail required. In the present paper we show an asy...

On the Maximum Principle for Harmonic Functions

Some generalizations of the maximum principle for harmonic functions are discussed. §

On Cooperative Elliptic Systems: Principal Eigenvalue and Characterization of the Maximum Principle

The purpose of this set of notes is to present the connection between the classical maximum principle with the principal eigenvalue of the elliptic operator. We will start with the maximum principle for single equations and proceed to the case of cooperative (or weakly-coupled) systems. By adopting an idea due to G. Sweers, we give a characterization of the principal eigenvalue for a cooperativ...