A Software for the Visualisationof Differential Geometry
In this paper we consider Riemannian manifolds of dimension , with semi-positive -curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green’s function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive -curvature. Modifying the test function construction of Esposito-Robert, we show...
We consider the integral functional , , where , , is a nonempty bounded connected open subset of with smooth boundary, and is a convex, differentiable function. We prove that if admits a minimizer in depending only on the distance from the boundary of , then must be a ball.