Pogorelov interior estimates for general sum-type Hessian equations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915867167555584 |
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| author | Dong, Weisong Xu, Sirui Zhang, Ruijia |
| author_facet | Dong, Weisong Xu, Sirui Zhang, Ruijia |
| contents | In this paper, we exploit the concavity of sums of Hessian operators to derive Pogorelov estimates for corresponding equations under the dynamic semi-convexity assumption, and we further obtain several Liouville-type results. Moreover, when k=n-1 and k=n we establish Pogorelov estimates in the admissible cone. As an application, we prove that any entire admissible solution in $\mathbb{R}^n$ with quadratic growth must be a quadratic polynomial. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_15345 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pogorelov interior estimates for general sum-type Hessian equations Dong, Weisong Xu, Sirui Zhang, Ruijia Analysis of PDEs Differential Geometry 35J15, 35B45, 35B08 In this paper, we exploit the concavity of sums of Hessian operators to derive Pogorelov estimates for corresponding equations under the dynamic semi-convexity assumption, and we further obtain several Liouville-type results. Moreover, when k=n-1 and k=n we establish Pogorelov estimates in the admissible cone. As an application, we prove that any entire admissible solution in $\mathbb{R}^n$ with quadratic growth must be a quadratic polynomial. |
| title | Pogorelov interior estimates for general sum-type Hessian equations |
| topic | Analysis of PDEs Differential Geometry 35J15, 35B45, 35B08 |
| url | https://arxiv.org/abs/2603.15345 |