Abstract
We make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces of revolution and ruled surfaces in R3. We prove that self-similar solutions of the MCF by non-cylindrical surfaces in R3 are trivial. Moreover, we characterize the self-similar solutions of the MCF by surfaces of revolutions under a homothetic helicoidal motion in R3 in terms of the curvature of the generating curve. Finally, we characterize the self-similar solutions for the MCF by cylindrical surfaces under a homothetic helicoidal motion in R3. Explicit families of exact solutions for the MCF by cylindrical surfaces in R3 are also given.
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