Non-convexity of level sets for solutions to $k$-Hessian equations in exterior domains
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914431551668224 |
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| author | Bo, Wang Cong, Wang Zhizhang, Wang |
| author_facet | Bo, Wang Cong, Wang Zhizhang, Wang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28138 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-convexity of level sets for solutions to $k$-Hessian equations in exterior domains Bo, Wang Cong, Wang Zhizhang, Wang Analysis of PDEs Differential Geometry 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. |
| title | Non-convexity of level sets for solutions to $k$-Hessian equations in exterior domains |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2603.28138 |