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15 June 2019 Interior C2 regularity of convex solutions to prescribing scalar curvature equations
Pengfei Guan, Guohuan Qiu
Duke Math. J. 168(9): 1641-1663 (15 June 2019). DOI: 10.1215/00127094-2019-0001

Abstract

We establish interior C2 estimates for convex solutions of the scalar curvature equation and the σ2-Hessian equation. We also prove interior curvature estimates for isometrically immersed hypersurfaces (Mn,g)Rn+1 with positive scalar curvature. These estimates are consequences of interior estimates for these equations obtained under a weakened condition.

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Pengfei Guan. Guohuan Qiu. "Interior C2 regularity of convex solutions to prescribing scalar curvature equations." Duke Math. J. 168 (9) 1641 - 1663, 15 June 2019. https://doi.org/10.1215/00127094-2019-0001

Information

Received: 29 November 2017; Revised: 6 December 2018; Published: 15 June 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07097311
MathSciNet: MR3961212
Digital Object Identifier: 10.1215/00127094-2019-0001

Subjects:
Primary: 35J60
Secondary: 35B45

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 9 • 15 June 2019
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