Stability of asymptotically conical gradient Kähler-Ricci expanders
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908581338546176 |
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| author | Chen, Longteng |
| author_facet | Chen, Longteng |
| contents | In this work, we consider a perturbation of an asymptotically conical gradient expanding Kähler-Ricci soliton metric $g$ in the same Kähler class. We demonstrate that, under suitable assumptions, the normalized Kähler-Ricci flow starting from the initial perturbed metric exists for all time and converges uniformly to an asymptotically conical gradient expanding Kähler-Ricci soliton metric $g_\infty$. Moreover, if the perturbed initial metric is asymptotic to $g$ at spatial infinity, then the limiting metric coincides with the original soliton, that is, $g_\infty = g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06850 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of asymptotically conical gradient Kähler-Ricci expanders Chen, Longteng Differential Geometry 53E20 In this work, we consider a perturbation of an asymptotically conical gradient expanding Kähler-Ricci soliton metric $g$ in the same Kähler class. We demonstrate that, under suitable assumptions, the normalized Kähler-Ricci flow starting from the initial perturbed metric exists for all time and converges uniformly to an asymptotically conical gradient expanding Kähler-Ricci soliton metric $g_\infty$. Moreover, if the perturbed initial metric is asymptotic to $g$ at spatial infinity, then the limiting metric coincides with the original soliton, that is, $g_\infty = g$. |
| title | Stability of asymptotically conical gradient Kähler-Ricci expanders |
| topic | Differential Geometry 53E20 |
| url | https://arxiv.org/abs/2510.06850 |