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arXiv · 2603.28138

Non-convexity of level sets for solutions to $k$-Hessian equations in exterior domains

Wang Bo·Wang Cong·Wang Zhizhang
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Abstract

In this paper, we provide examples to show that for $1 \leq k \leq n/2$, solutions to $k$-Hessian equations $S_k(D^2u)=1$ in the exterior of a strictly convex domain need not be quasiconvex, when prescribing quadratic growth at infinity. Additionally, we give a new proof for the quasiconvexity of harmonic functions in such exterior domains that decay to zero at infinity.

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Wang Bo, Wang Cong, Wang Zhizhang. 2026-03-30. Non-convexity of level sets for solutions to $k$-Hessian equations in exterior domains. https://arxiv.org/abs/2603.28138

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