Revista Matemática Iberoamericana


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Volume 33, Issue 2, 2017, pp. 547–554
DOI: 10.4171/RMI/948

A note on star-shaped compact hypersurfaces with prescribed scalar curvature in space forms

Joel Spruck[1] and Ling Xiao[2]

(1) The Johns Hopkins University, Baltimore, USA
(2) Rutgers University, 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