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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1305.2669 |
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| _version_ | 1866913321164210176 |
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| author | Chen, Chuanqiang Ma, Xi-Nan Shi, Shujun |
| author_facet | Chen, Chuanqiang Ma, Xi-Nan Shi, Shujun |
| contents | For the Monge-Ampère equation $\det D^2 u=1$, we find new auxiliary curvature functions which attain respective maximum on the boundary. Moreover, we obtain the upper bounded estimates for the Gauss curvature and mean curvature of the level sets for the solution to this equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1305_2669 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Curvature estimates for the level sets of solutions of the Monge-Ampère equation $\det D^2 u=1$ Chen, Chuanqiang Ma, Xi-Nan Shi, Shujun Analysis of PDEs 35J65 For the Monge-Ampère equation $\det D^2 u=1$, we find new auxiliary curvature functions which attain respective maximum on the boundary. Moreover, we obtain the upper bounded estimates for the Gauss curvature and mean curvature of the level sets for the solution to this equation. |
| title | Curvature estimates for the level sets of solutions of the Monge-Ampère equation $\det D^2 u=1$ |
| topic | Analysis of PDEs 35J65 |
| url | https://arxiv.org/abs/1305.2669 |