Geodesic
Bifurcations of spherically asymmetric solutions to an evolution equation for curves
Takeo Sugai1
1Tokyo Institute of Technology, Japan
Interfaces and free boundaries, Tome 24 (2022) no. 2, pp. 287-306

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DOI

We show that a certain non-local curvature flow for planar curves has non-trivial self-similar solutions with n-fold rotational symmetry, bifurcated from a trivial circular solution. Moreover, we show that the trivial solution is stable with respect to perturbations which keep the geometric center and the enclosed area, and that, for n different from 3, the n-fold symmetric solution is stable with respect to perturbations which satisfy the same conditions as above and have the same symmetry as the solutions.
DOI : 10.4171/ifb/474
Classification : 35-XX
Mots-clés : Self-similar solutions, linearized stability, bifurcation solutions, curve shortening flow

Takeo Sugai  1

1 Tokyo Institute of Technology, Japan 
Takeo Sugai. Bifurcations of spherically asymmetric solutions to an evolution equation for curves. Interfaces and free boundaries, Tome 24 (2022) no. 2, pp. 287-306. doi: 10.4171/ifb/474
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     year = {2022},
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     number = {2},
     doi = {10.4171/ifb/474},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/474/}
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