关于带临界强制项的广义 BV 平均曲率流的注记
A note on generalized BV mean curvature flow with a critical forcing term
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中文总结 AI 辅助
本文注记证明了Liu–Tonegawa的带临界强制项的弱平均曲率流是广义BV流，确定了Brakke流满足面积变化公式的最小条件，推导了相关流的灭绝时间下界并概述了紧性定理的证明。
中文摘要 AI 辅助
在本注记中，我们证明了Liu–Tonegawa（2024）得到的带临界强制项的弱平均曲率流满足 BV 型面积变化公式，即该流不仅是 Brakke 流，还是 Stuvard–Tonegawa（2024）提出的广义 BV 流。为建立该结果，我们确定了 Brakke 流满足面积变化公式的最小条件。作为主定理的应用，我们推导了带临界强制项的广义 BV 流的灭绝时间下界，还概述了广义 BV 流紧性定理的证明。
英文摘要
In this note, we show that a weak mean curvature flow with critical forcing term obtained by Liu--Tonegawa (2024) satisfies the BV-type area change formula, that is, their flow is not only a Brakke flow but also a generalized BV flow, which is proposed by Stuvard--Tonegawa (2024). To establish this result, we identify minimal conditions under which a Brakke flow satisfies the area-change formula. As an application of our main theorem, we derive a lower bound for the extinction time of generalized BV flows with a critical forcing term. We also outline the proof of a compactness theorem for generalized BV flows.
