Evolution of Contractions between Non-Compact Manifolds

Research output: Working paperResearch


Let N be a complete manifold with bounded geometry, such that secN≤−σ<0 for some positive constant σ. We investigate the mean curvature flow of the graphs of smooth length-decreasing maps f:Rm→N. In this case, the solution exists for all times and the evolving submanifold stays the graph of a length-decreasing map ft. We further prove uniform decay estimates for all derivatives of order ≥2 of ft along the flow.
Original languageEnglish
PublisherarXiv preprint
Publication statusUnpublished - 2018
Externally publishedYes
SeriesarXiv

    Research areas

  • math.DG, 53C44 (Primary) 53C42, 53C21 (Secondary)

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ID: 291609988