JournalsifbVol. 16, No. 1pp. 41–64

Stability and bifurcation of equilibria for the axisymmetric averaged mean curvature flow

  • Jeremy LeCrone

    Kansas State University, Manhattan, USA
Stability and bifurcation of equilibria for the axisymmetric averaged mean curvature flow cover
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Abstract

We study the averaged mean curvature flow, also called the volume preserving mean curvature flow, in the particular setting of axisymmetric surfaces embedded in R3\mathbb R^3 satisfying periodic boundary conditions. We establish analytic well-posedness of the flow within the space of little-Hölder continuous surfaces, given rough initial data. We also establish dynamic properties of equilibria, including stability, instability, and bifurcation behavior of cylinders, where the radius acts as a bifurcation parameter.

Cite this article

Jeremy LeCrone, Stability and bifurcation of equilibria for the axisymmetric averaged mean curvature flow. Interfaces Free Bound. 16 (2014), no. 1, pp. 41–64

DOI 10.4171/IFB/313