A Loewner-Nirenberg phenomena for Ricci flow on compact manifolds with boundary.II
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| Format: | Preprint |
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2026
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| _version_ | 1866911672701026304 |
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| author | Li, Gang |
| author_facet | Li, Gang |
| contents | This is a continuation of the research in [16]. Let $(\overline{M},g_{-1})$ be a closed geodesic $r_0$-ball in the hyperbolic space $(\mathbb{H}^n,g_{-1})$. Let $m\neq1$ be a positive constant. In this paper, we show that for $n\geq3$, starting from the metric $m g_{-1}$ on $\overline{M}$, with certain prescribed non-decreasing rotationally symmetric mean curvature and the fixed conformal class $[g_{\mathbb{S}^{n-1}}]$ on the boundary $\partial M$, the solution $g(t)$ to the normalized Ricci flow $(1.2)$ which is continuous up to the boundary, exists for all $t>0$, and converges locally uniformly in the interior $M$ of $\overline{M}$ to a complete hyperbolic metric as $t\to\infty$(see Theorem 1.1 for details). Under some additional conditions, we show the same conclusion holds for $n=2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_20383 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Loewner-Nirenberg phenomena for Ricci flow on compact manifolds with boundary.II Li, Gang Differential Geometry Analysis of PDEs This is a continuation of the research in [16]. Let $(\overline{M},g_{-1})$ be a closed geodesic $r_0$-ball in the hyperbolic space $(\mathbb{H}^n,g_{-1})$. Let $m\neq1$ be a positive constant. In this paper, we show that for $n\geq3$, starting from the metric $m g_{-1}$ on $\overline{M}$, with certain prescribed non-decreasing rotationally symmetric mean curvature and the fixed conformal class $[g_{\mathbb{S}^{n-1}}]$ on the boundary $\partial M$, the solution $g(t)$ to the normalized Ricci flow $(1.2)$ which is continuous up to the boundary, exists for all $t>0$, and converges locally uniformly in the interior $M$ of $\overline{M}$ to a complete hyperbolic metric as $t\to\infty$(see Theorem 1.1 for details). Under some additional conditions, we show the same conclusion holds for $n=2$. |
| title | A Loewner-Nirenberg phenomena for Ricci flow on compact manifolds with boundary.II |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2604.20383 |