We study the crystalline curvature flow of planar networks with a single hexagonal anisotropy. After proving the local existence of a classical solution for a rather large class of initial conditions, we classify the homothetically shrinking solutions having one bounded component. We also provide some examples of networks shrinking to a segment with higher multiplicity.
Bellettini, G., Kholmatov, S.Yu., Almuratov, F.M. (2025). Crystalline Hexagonal Curvature Flow of Networks: Short-Time, Long-Time, and Self-Similar Evolutions. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 57(4), 4459-4518 [10.1137/20m1360529].
Crystalline Hexagonal Curvature Flow of Networks: Short-Time, Long-Time, and Self-Similar Evolutions
Bellettini, Giovanni;
2025-01-01
Abstract
We study the crystalline curvature flow of planar networks with a single hexagonal anisotropy. After proving the local existence of a classical solution for a rather large class of initial conditions, we classify the homothetically shrinking solutions having one bounded component. We also provide some examples of networks shrinking to a segment with higher multiplicity.
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https://hdl.handle.net/11365/1299154