Existence and uniqueness of (p,k)-convex hypersurfaces are established for Hessian quotient type curvature equations via a priori estimates, continuity method, and an inverse convexity property yielding a constant rank theorem for strict convexity.
Firey, The determination of convex bodies from their mean radius of curvature functions, Mathematika, 14(1), 1-13, (1967)
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The existence of $(\mathbf{p}, k)$-convex hypersurfaces for a class of Hessian quotient type curvature equations
Existence and uniqueness of (p,k)-convex hypersurfaces are established for Hessian quotient type curvature equations via a priori estimates, continuity method, and an inverse convexity property yielding a constant rank theorem for strict convexity.