the paper concerns the relations between the relative Manin-Mumford conjecture and Pink’s conjecture on unlikely intersections in mixed Shimura varieties. The variety under study is the 4-dimensional Poincaré biextension attached to a universal elliptic curve. A detailed list of its special subvarieties is drawn up, providing partial verifications of Pink’s conjecture in this case, and two open...

This paper presents a Meyer–Vietoris type gluing formula for conformal invariant of Riemannian surface with boundary that is defined by the determinant Dirichlet-to-Neumann operator. The used to bound asymptotics under degeneration. It shown associated height function on moduli space hyperbolic surfaces geodesic proper only in genus zero. Properness implies compactness theorem Steklov isospectr...

In the present paper we develop an approach to obtain sharp spectral asymptotics for Steklov type problems on planar domains with corners. Our main focus is two-dimensional sloshing problem, which a mixed Steklov—Neumann boundary value problem describing small vertical oscillations of ideal fluid in container or canal uniform cross-section. We prove two-term asymptotic formula eigenvalues. part...

We continue the work of Camano et al . [ SIAM J. Math. Anal. 49 (2017) 4376–4401] on electromagnetic Steklov eigenvalues. The authors recognized that in general eigenvalues do not correspond to spectrum a compact operator and hence proposed modified eigenvalue problem with desired properties. present article considers original problem. cast problems as for holomorphic function A (?). construct ...

The stress-driven grain boundary diffusion problem is a continuum model of mass transport phenomena in microelectronic circuits due to high current densities (electromigration) and gradients in normal stress along grain boundaries. The model involves coupling many different equations and phenomena, and difficulties such as nonlocality, complex geometry, and singularities in the stress tensor ha...

We study the recursion (aka Schur) parameters for monic polynomials orthogonal on the unit circle with respect to a weight which provides negative answer to the conjecture of Steklov.