Non–existence of theta–shaped self–similarly shrinking networks moving by curvature

@article{Baldi2016NonexistenceOT,
  title={Non–existence of theta–shaped self–similarly shrinking networks moving by curvature},
  author={P. Baldi and E. Haus and C. Mantegazza},
  journal={Communications in Partial Differential Equations},
  year={2016},
  volume={43},
  pages={403 - 427}
}
ABSTRACT We prove that there are no networks homeomorphic to the Greek “Theta” letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees, such that under the motion by curvature they are self–similarly shrinking. This fact completes the classification of the self–similarly shrinking networks in the plane with at most two triple junctions, see [5, 10, 25, 2]. 

References

SHOWING 1-10 OF 47 REFERENCES
Networks Self-Similarly Moving by Curvature with Two Triple Junctions
Evolution of spoon-shaped networks
Evolution of convex lens-shaped networks under the curve shortening flow
Motion by Curvature of Planar Networks
Curvature evolution of nonconvex lens-shaped domains
Motion by curvature of networks with two triple junctions
...
1
2
3
4
5
...