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Generalized Minkowski inequality via degenerate Hessian equations on exterior domains

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arxiv 2207.05673 v1 pith:LD6JJM4B submitted 2022-07-12 math.DG

Ling Xiao This is my paper · ORCID
classification math.DG
keywords degeneratedomainexteriorgeneralizedhessianinequalityminkowskiomega
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abstract

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

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exterior Dirichlet problem for Hessian equations on a non-convex ring

    math.AP 2025-07 conditional novelty 6.0 of 10

    The exterior Dirichlet problem for Hessian equations admits a unique smooth k-convex solution when the obstacle is star-shaped and strictly (k-1)-convex, not necessarily convex, for 2 <= k <= n.

  2. General monotone formula for homogeneous $k$-Hessian equation in the exterior domain and its applications

    math.AP 2025-06 conditional novelty 6.0 of 10

    A new monotone formula for the k-Hessian equation yields ball characterizations for exterior overdetermined problems and recovers sharp geometric inequalities.

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