Topological arguments in prescribing the scalar curvature under minimal boundary mean curvature condition on $S^n_+$

Abstract

This paper is devoted to the prescribed scalar curvature problem under minimal boundary mean curvature condition on the standard $n$-dimensional half Sphere, with $n\geq 3.$ Using tools related to the theory of critical points at infinity, we provide some topological conditions, on the level sets of a given positive function on $S_+^n$, under which we prove some existence results.