5 papers
Algebraic defect and positive mother body measures
Boris Shapiro
Continuing the study of mother-body measures with algebraic Cauchy transform, we associate with a positive algebraic germ , its irreducible equation , and a compact co…
Van Vleck spectra of high-order Heun operators:\ finite-band universality and exterior asymptotics
Boris Shapiro
We study high-order analogues of the classical Heun operator of Fuchs index one, \[ \dq=\sum_{i=1}^k Q_i(z)\frac{d^i}{dz^i}, \qquad °Q_i\le i+1, \qquad °Q_k=k+1. \] For a fixed deg…
Frenet turns
Boris Shapiro
We discuss a problem posed by A.~Agrachev asking how many times a usual circle in should be traversed to admit a deformation by curves with nowhere degenerating Frene…
Ribbon graphs and meromorphic functions
B. Shapiro
Let Y be a compact Riemann surface, phi:Y -> CP^1 a meromorphic function, and Gamma in Y a ribbon graph avoiding the critical points of phi. Then phi(Gamma) is an immersed graph in…
The translation geometry of Pólya's shires
Rikard Bøgvad, Boris Shapiro, Guillaume Tahar +1
In his shire theorem, G. Pólya proves that the zeros of iterated derivatives of a meromorphic function in the complex plane accumulate on the union of edges of the Voronoi diagram…