| Abstract: |
| We report some existence and regularity results on the multi-phase mean curvature flow in the standard hyperbolic space of general dimensions. Under a mild regularity assumption on the initial data, we prove the global-in-time existence and regularity results of the mean curvature flow. In particular, we show that the smoothness of the asymptotic boundary of the mean curvature flow persists for all time if the initial data is smooth. This reveals an interesting time-dependent regularity property different from the static case where the dimension plays an important role. |
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