Um princípio de tangência e aplicações

Abstract

We present tools, such as a maximum principle for elliptic functions and properties of a-hyperbolic polynomials, to study a tangency principle between two hypersurfaces with r-mean curvatures of a Riemannian manifold, which gives sufficient geometric conditions for these hypersurfaces to coincide in a neighborhood of a tangency point. We also study the problem of calculating the r-mean curvatures of the geodesic sphere, to use it in applications of the tangency principle.