Timeline for Distance function to mean curvature flow

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Dec 15, 2022 at 15:58	comment	added	Leo Moos		I meant update in the sense that one might have to change $\gamma$ that was chosen on the previous page, 'so small that [...] $r$ is smooth on the set $U$', to a smaller value. I didn't mean that $\gamma$ would have to be updated along the flow. (Is that how you read my comment? That's how I interpreted your reply, anyway.) I didn't mean the question as a gotcha - obviously the size of $U$ plays no role in the argument, which is fine as is. I was just wondering whether I'd missed something, and the inequality really does hold wherever $r$ is smooth.
Dec 15, 2022 at 15:28	comment	added	RBega2		Why would it need to be updated? You are trying to get avoidance on a compact time interval and have a smooth compact flow so you just choose $\gamma$ small enough initially so the differential inequality is satisfied (I guess this should have been made more explicit and may be a gap/oversight in the proof but seems easy to fix).
Dec 15, 2022 at 8:10	comment	added	Leo Moos		Sure, but the size of the neighborhood isn't updated - the only thing imposed on it is that it be narrow enough that the Brakke flow and $Q$ do not initially intersect there, and that $r$ be smooth on it.
Dec 15, 2022 at 0:23	history	answered	RBega2	CC BY-SA 4.0