Existence and uniqueness of strictly spherically convex solutions is proved for the Lp dual Christoffel-Minkowski problem involving the Hessian quotient operator via an inverse convexity full rank theorem and a priori estimates.
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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.
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The $L_p$ dual Christoffel-Minkowski type problem for a class of Hessian quotient equations
Existence and uniqueness of strictly spherically convex solutions is proved for the Lp dual Christoffel-Minkowski problem involving the Hessian quotient operator via an inverse convexity full rank theorem and a priori estimates.
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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.