Generalized Minkowski inequality via degenerate Hessian equations on exterior domains

In this paper, we prove a generalized Minkowski inequality holds for any smooth, $(k-1)$-convex, starshaped domain $Ω.$ Our proof relies on the solvability of the degenerate $k$-Hessian equation on the exterior domain $\mathbb R^n\setminusΩ.$

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