A note on starshaped compact hypersurfaces with a prescribed scalar curvature in space forms

Abstract

In [7], Guan, Ren and Wang obtained a $C^2$ a priori estimate for admissible 2-convex hypersurfaces satisfying the Weingarten curvature equation ${\sigma }_2(\kappa (X))=f(X,\nu (X)).$ In this note, we give a simpler proof of this result, and extend it to space forms.