Interior \(C^2\) regularity of convex solutions to prescribing scalar curvature equations

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Abstract: We establish interior

C^{2}

estimates for convex solutions of scalar curvature equation and

s i g m a_{2}

-Hessian equation. We also prove interior curvature estimate for isometrically immersed hypersurfaces

(M^{n}, g) s u b s e t m a t h b b R^{n + 1}

with positive scalar curvature. These estimates are consequences of an interior estimate for these equations obtained under a weakened condition.

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