Revista Matemática Iberoamericana
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A note on star-shaped compact hypersurfaces with prescribed scalar curvature in space formsJoel Spruck and Ling Xiao (1) Department of Mathematics, The Johns Hopkins University, 3400 N. Charles St., MD 21218, Baltimore, USA
(2) Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., NJ 08854, Piscataway, USA
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.
Keywords: Scalar curvature, space forms
Spruck Joel, Xiao Ling: A note on star-shaped compact hypersurfaces with prescribed scalar curvature in space forms. Rev. Mat. Iberoamericana 33 (2017), 547-554. doi: 10.4171/RMI/948