Journal of Evolution Equations

, Volume 10, Issue 1, pp 21–27 | Cite as

Loss of convexity and embeddedness for geometric evolution equations of higher order



We show that for a large class of geometric evolution equations of immersed surfaces in the Euclidean space, there are compact embedded surfaces that lose their embeddedness and compact strictly convex surfaces that lose their convexity under these evolution equations.

Mathematics Subject Classification (2000)

Primary: 53C44 Secondary: 35K55 


Geometric evolution equations Nonlinear parabolic equations 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Albert-Einstein InstitutPostdam-GolmGermany

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