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math.AP2025
Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions
Giovanni Bellettini, Shokhrukh Yu. Kholmatov, Matteo Novaga
Given a planar crystalline anisotropy, we study the crystalline elastic flow of immersed polygonal curves, possibly also unbounded. Assuming that the segments evolve by parallel tr…
math.AP2025
A De Giorgi conjecture on the regularity of minimizers of Cartesian area in 1D
Giovanni Bellettini, Shokhrukh Yu. Kholmatov
We prove a -regularity of minimizers of the functional provided is a bounded open inte…
math.SP2025
Bound states of 2+1 fermionic trimers on lattice at strong couplings
Janikul Abdullaev, Ahmad Khalkhuzhaev, Shokhrukh Yu. Kholmatov
In this paper, we investigate the bound states of fermionic trimers on a three-dimensional lattice at strong coupling. Specifically, we analyze the discrete spectrum of the a…