Loss of convexity and embeddedness for geometric evolution equations of higher order
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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
KeywordsGeometric evolution equations Nonlinear parabolic equations
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