Helicoidal surfaces rotating/translating under the mean curvature flow
Name
10711_2012_Article_9716.pdf
Size
677.48 KB
Format
Adobe PDF
Checksum (MD5)
153ddf092c2929a7cb5c675b43257ec4
Author(s)
Halldorsson, Hoeskuldur Petur
Date Issued
March 2012
Journal
Geometriae Dedicata
Publisher
Springer Netherlands
Citation
Halldorsson, Hoeskuldur P. “Helicoidal Surfaces Rotating/translating Under the Mean Curvature Flow.” Geom Dedicata 162, no. 1 (March 17, 2012): 45–65.
Version
Author's final manuscript
Abstract
We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new two-parameter family of immersed helicoidal surfaces that rotate/translate with constant velocity under the flow. We look at their limiting behaviour as the pitch of the helicoidal motion goes to 0 and compare it with the limiting behaviour of the classical helicoidal minimal surfaces. Finally, we give a classification of the immersed cylinders in the family of constant mean curvature helicoidal surfaces.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10711-012-9716-2
