$C^0$收敛下质量的下半连续性性和Huisken等周质量
Lower semicontinuity of mass under $C^0$ convergence and Huisken's isoperimetric mass
摘要：
给定一列具有最小边界的非负数量曲率的渐近平坦3-流形，在点$C^0$ Cheeger-Gromov意义下收敛到渐近平坦极限空间，证明了该极限的总质量由该序列的总质量的limif上界.换句话说，在这种收敛下，总质量是较低连续的。为了证明这一点，我们使用Huisken的等周质量的概念，连同修改后的弱中曲率流参数。我们包括一个简短的讨论Huisken的工作之前，解释我们的工作扩展。结果都是针对三维的。
英文摘要：
Given a sequence of asymptotically flat 3-manifolds of nonnegative scalar curvature with outermost minimal boundary, converging in the pointed $C^0$ Cheeger--Gromov sense to an asymptotically flat limit space, we show that the total mass of the limit is bounded above by the liminf of the total masses of the sequence. In other words, total mass is lower semicontinuous under such convergence. In order to prove this, we use Huisken's isoperimetric mass concept, together with a modified weak mean curvature flow argument. We include a brief discussion of Huisken's work before explaining our extension of that work. The results are all specific to three dimensions.
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