We study the averaged mean curvature ow, also called the volume preserving mean curvature ow, in the particular setting of axisymmetric surfaces embedded in R3 satisfying periodic boundary conditions. We establish analytic well-posedness of the ow within the space of little-Holder 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.
Copyright © 2014, European Mathematical Society Publishing House. Article first published online: 2014.
The definitive version is available at:
Lecrone, Jeremy. "Stability and Bifurcation of Equilibria for the Axisymmetric Averaged Mean Curvature Flow." Interfaces and Free Boundaries 16, no. 1 (2014): 41-64. doi:10.4171/ifb/313.
LeCrone, Jeremy, "Stability and Bifurcation of Equilibria for the Axisymmetric Averaged Mean Curvature Flow" (2014). Math and Computer Science Faculty Publications. 163.