Monge-Ampère equations with right-hand sides of polynomial growth
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909214400577536 |
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| author | Choi, Beomjun Choi, Kyeongsu Kim, Soojung |
| author_facet | Choi, Beomjun Choi, Kyeongsu Kim, Soojung |
| contents | We study the regularity and the growth rates of solutions to two-dimensional Monge-Ampère equations with the right-hand side exhibiting polynomial growth. Utilizing this analysis, we demonstrate that the translators for the flow by sub-affine-critical powers of the Gauss curvature are smooth, strictly convex entire graphs. These graphs exhibit specific growth rates that depend solely on the power of the flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01040 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monge-Ampère equations with right-hand sides of polynomial growth Choi, Beomjun Choi, Kyeongsu Kim, Soojung Analysis of PDEs Differential Geometry 53E99, 35J96 We study the regularity and the growth rates of solutions to two-dimensional Monge-Ampère equations with the right-hand side exhibiting polynomial growth. Utilizing this analysis, we demonstrate that the translators for the flow by sub-affine-critical powers of the Gauss curvature are smooth, strictly convex entire graphs. These graphs exhibit specific growth rates that depend solely on the power of the flow. |
| title | Monge-Ampère equations with right-hand sides of polynomial growth |
| topic | Analysis of PDEs Differential Geometry 53E99, 35J96 |
| url | https://arxiv.org/abs/2404.01040 |