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Evolution of highly symmetric curves under the shrinking curvature flow
Author(s) -
Chen Wenyan,
Wang Xiaoliu,
Yang Ming
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4262
Subject(s) - mathematics , regular polygon , curvature , mean curvature flow , flow (mathematics) , mathematical analysis , convex function , pure mathematics , geometry , mean curvature
Under the shrinking curvature flow with inner normal velocity V = k α ( α > 1), it is shown that highly symmetric, locally convex initial curves evolve into a point asymptotically like an multi‐circles. The proof relies on a crucial use of Bonnensen inequality for highly symmetric, locally convex curves. Copyright © 2016 John Wiley & Sons, Ltd.