The paper proves an interior bound on principal curvatures for convex graphs solving the curvature quotient equation σ_n/σ_{n-2}=f in all dimensions n≥3.
Caffarelli, Louis Nirenberg, and Joel Spruck, The Dirichlet problem for nonlinear second order elliptic equations
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Interior curvature estimate for curvature quotient equations on convex hypersurfaces
The paper proves an interior bound on principal curvatures for convex graphs solving the curvature quotient equation σ_n/σ_{n-2}=f in all dimensions n≥3.