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For a manifold-with-boundary moving by mean curvature flow, the entropy at alater time is bounded by the entropy at an earlier time plus a boundary term.This paper controls the boundary term in a geometrically natural way. Inparticular, it shows (under mild hypotheses)that the entropy of a compacttranslator is less than or equal to the entropy of the boundary plus themaximal cone density of the boundary.

The Boundary Term in Huisken's Monotonicity Formula and the Entropy of Translators