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摘要
For mean curvature flows in Euclidean spaces, Brian White proved a regularity theorem which gives C-2,C-alpha estimates in regions of spacetime where the Gaussian density is close enough to 1. This is proved by applying Huisken%26apos;s monotonicity formula. Here we will consider mean curvature flows in semi-Euclidean spaces, where each spatial slice is an m-dimensional graph in R-n(m+n) satisfying a gradient bound stronger than the spacelike condition. By defining a suitable quantity to replace the Gaussian density ratio, we prove monotonicity theorems similar to Huisken%26apos;s and use them to prove a regularity theorem similar to White%26apos;s.
- 出版日期2012-2
