Geodesic
Stability and bifurcation of equilibria for the axisymmetric averaged mean curvature flow
Jeremy LeCrone1
1Kansas State University, Manhattan, USA
Interfaces and free boundaries, Tome 16 (2014) no. 1, pp. 41-64

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DOI

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 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.
DOI : 10.4171/ifb/313
Classification : 35-XX, 53-XX
Mots-clés : Averaged mean curvature flow, periodic boundary conditions, maximal regularity, nonlinear stability, bifurcation

Jeremy LeCrone  1

1 Kansas State University, Manhattan, USA 
Jeremy LeCrone. Stability and bifurcation of equilibria for the axisymmetric averaged mean curvature flow. Interfaces and free boundaries, Tome 16 (2014) no. 1, pp. 41-64. doi: 10.4171/ifb/313
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     title = {Stability and bifurcation of equilibria for the axisymmetric averaged mean curvature flow},
     journal = {Interfaces and free boundaries},
     pages = {41--64},
     year = {2014},
     volume = {16},
     number = {1},
     doi = {10.4171/ifb/313},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/313/}
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