Crystalline Hexagonal Curvature Flow of Networks: Short-Time, Long-Time, and Self-Similar Evolutions
Giovanni BellettiniDepartment of Mathematics, University of Siena, via Roma 56, 53100 Siena, Italy, and International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151, Trieste, ItalyShokhrukh Yu. KholmatovFaculty of Mathematics, University of Vienna, Oskar-Morgenstern Platz 1, 1090 Vienna, Austria, and Samarkand State University, University Boulevard 15, 140104 Samarkand, UzbekistanFirdavsjon M. AlmuratovJizzakh Branch of the National University of Uzbekistan, Sh. Rashidov Avenue, 259 130100, Jizzakh, Uzbekistan
ABI
Аннотация
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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