Revista Matemática Iberoamericana
Full-Text PDF (183 KB) | Metadata | Table of Contents | RMI summary
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, UNITED STATES
(2) Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., NJ 08854, PISCATAWAY, UNITED STATES
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