Universal Hardy–Sobolev inequalities on hypersurfaces of Euclidean space
Universal Hardy–Sobolev inequalities on hypersurfaces of Euclidean space
In this paper, we study Hardy–Sobolev inequalities on hypersurfaces of [Formula: see text], all of them involving a mean curvature term and having universal constants independent of the hypersurface. We first consider the celebrated Sobolev inequality of Michael–Simon and Allard, in our codimension one framework. Using their ideas, but simplifying …