manuscripta mathematica

, Volume 126, Issue 3, pp 333–351

Forced convex mean curvature flow in Euclidean spaces

Article

DOI: 10.1007/s00229-008-0181-z

Cite this article as:
Li, G. & Salavessa, I. manuscripta math. (2008) 126: 333. doi:10.1007/s00229-008-0181-z

Abstract

We show the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term may shrink to a point in finite time if the forcing term is small, or exist for all times and expand to infinity if the forcing term is large enough. The flow can converge to a round sphere in special cases. Long time existence and convergence of the normalization of the flow are studied.

Mathematics Subject Classification (2000)

Primary 53C4435K55Secondary 53A05

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceHubei UniversityWuhanPeople’s Republic of China
  2. 2.Centro de Física das Interacções FundamentaisInstituto Superior Técnico, Technical University of LisbonLisboaPortugal