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Evolution of Area-Decreasing Maps Between Two-Dimensional Euclidean Spaces

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We consider the mean curvature flow of the graph of a smooth map f: R2→ R2 between two-dimensional Euclidean spaces. If f satisfies an area-decreasing property, the solution exists for all times and the evolving submanifold stays the graph of an area-decreasing map ft. Further, we prove uniform decay estimates for the mean curvature vector of the graph and all higher-order derivatives of the corresponding map ft.

OriginalsprogEngelsk
TidsskriftJournal of Geometric Analysis
Vol/bind28
Udgave nummer4
Sider (fra-til)3928-3949
Antal sider22
ISSN1050-6926
DOI
StatusUdgivet - 15 dec. 2018
Eksternt udgivetJa

ID: 233725579