Related papers: Explicit equations of the Cartwright-Steger surfac…
A class of generalized Schr\"{o}dinger elliptic problems involving concave-convex and other types of nonlinearities is studied. A reasonable overview about the set of solutions is provided when the parameters involved in the equation assume…
The notion of a symplectic expansion directly relates the topology of a surface to formal symplectic geometry. We give a method to construct a symplectic expansion by solving a recurrence formula given in terms of the…
We discuss K3 surfaces in characteristic two that contain the Kummer configuration formed by smooth rational curves on it.
We consider Fokker-Planck equations that interpolate a pair of supersymmetrically related Fokker-Planck equations with constant coefficients. Based on the interesting property of shape-invariance, various one-parameter interpolations of the…
In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bezier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a…
We construct tilt stability conditions on surface root stacks and show that they have support property with respect to the rational Chen-Ruan cohomology.
Counterparts of the Dyson-Schwinger equations for scalar QED in an external electromagnetic field are derived. Exact structure and diagrammatic interpretation of the corresponding mass and polarization operators are obtained. It is shown…
Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the Navier-Stokes equations to system of differential equations in three, two, and one independent variables. The large sets of exact solutions of the Navier-Stokes…
We give conditions for regularity of solutions of three dimensional incompressible Navier-Stokes equations based on the pressure and on structure functions.
This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of…
We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry…
We construct an explicit K3 surface over the field of rational numbers that has geometric Picard rank one, and for which there is a transcendental Brauer-Manin obstruction to weak approximation. To do so, we exploit the relationship between…
We provide explicit equations and parameterizations of some new rational Gushel-Mukai fourfolds of special type.
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
In recent literature several derivations of incompressible Navier-Stokes type equations that model the dynamics of an evolving fluidic surface have been presented. These derivations differ in the physical principles used in the modeling…
For any positive integer $r$, we construct a smooth complex projective rational surface which has at least $r$ real forms not isomorphic over $\mathbb{R}$.
We give some estimate of type sup*inf for scalar curvature type equations.
We present explicit equations of semi-stable elliptic surfaces (i.e., having only type $I_n$ singular fibers) which are associated to the torsion-free genus zero congruence subgroups of the modular group as classified by A. Sebbar.
In this paper, we classify the rotational surfaces with constant skew curvature in $3$-space forms. We also give a variational characterization of the profile curves of these surfaces as critical points of a curvature energy involving the…
We determine the Lie point symmetries of the Fokker-Planck equation and provide examples of solutions of this equation. The Fokker-Planck equation admits a conserved form, hence there is an auxiliary system associated to this equation and…