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

By J. Spruck, Ling Xiao. 2015

57 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/61d87e149ae284a8a90dedd52fe1ad24a4bc9caa

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

The global curvature estimate for the n-2 Hessian equation (2020, background): “Spruck-Xiao [45] established the curvature estimate for the prescribed scalar curvature problem in space forms and gave a simple proof of our curvature estimate for the same equation in the Euclidean space.”
A second order estimate for general complex Hessian equations (2015, background): “al Hessian equations when 2 <k<n. If k= 2, Guan-RenWang [9] removed the convexity assumption by investigating the structure of the operator. A simpler argument was given recently by Spruck-Xiao [18]. However, the arguments are not applicable to the complex case due to the diﬀerence between the”