论文标题
末日定期定理Brakke流
End-time regularity theorem for Brakke flows
论文作者
论文摘要
对于一般的$ k $二维的brakke流，从$ \ mathbb {r}^n $中，从本地接近$ k $二维平面，从衡量意义上讲，证明该流程在当地的平面图中以平滑的图表表示，并且对所有衍生词的估计都达到了最终时间。此外，在时空的任何时候高斯密度接近$ 1 $，流量可以顺利扩展，因为平均曲率流到社区中的那个时候：这将怀特的本地规则定理扩展到了Brakke Flow。实际上，根据平均曲率以及在尺寸敏锐的可集成性类别或Hölder类中的额外强迫术语驱动的更一般的Brakke样流程实际上是获得了规律性结果。
For a general $k$-dimensional Brakke flow in $\mathbb{R}^n$ locally close to a $k$-dimensional plane in the sense of measure, it is proved that the flow is represented locally as a smooth graph over the plane with estimates on all the derivatives up to the end-time. Moreover, at any point in space-time where the Gaussian density is close to $1$, the flow can be extended smoothly as a mean curvature flow up to that time in a neighborhood: this extends White's local regularity theorem to general Brakke flows. The regularity result is in fact obtained for more general Brakke-like flows, driven by the mean curvature plus an additional forcing term in a dimensionally sharp integrability class or in a Hölder class.
