Related papers: Integrable Models on Hyper-Elliptic Surfaces
We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general…
We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with…
We compute some numerical invariants of the lines on hyperplane sections of a smooth cubic threefold over complex numbers. We also prove that for any smooth hypersurface $X\subset \mathbb P^{n+1}$ of degree $d$ over an algebraically closed…
We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.
We give a rigorous proof of the validity of the point vortex description for a class of inviscid generalized surface quasi-geostrophic models on the whole plane.
We derive level set version of partial uniform ellipticity for symmetric concave functions. This suggests an effective approach to investigate second order fully nonlinear equations of elliptic and parabolic type.
The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing Inertial Manifolds for such type of problems is suggested…
We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is…
We study the non-embddability property for a class of real hypersurfaces, called real hypersurfaces of involution type, into the sphere in the low codimensional case, by making use of property of a naturally related Gauss curvature. We also…
The aim of the paper is to provide a series of new examples of smooth surfaces in P^4, not of general type, in degrees varying from 12 up to 14, and to describe their geometry. By using mainly syzygies and liaison techniques, we construct…
We discuss the parabolic Hilbert scheme of points on smooth surface, which is an interesting generalization of Hilbert scheme of points on surface. Some of the studies by Ellingsrud-Stromme, Goettsche, Cheah, Nakajima and Grojnowski can be…
After quick survey of some key results and open questions about the structure of singularities of minimal surfaces, we discuss recent work~\cite{Sim23} on singularities of stable minimal hypersurfaces, including some simplifications of the…
We construct integrable pseudopotentials with an arbitrary number of fields in terms of elliptic generalization of hypergeometric functions in several variables. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic…
We construct examples of flat surfaces in $\mathbb{H}^3$ which are graphs over a two-punctured horosphere and classify complete embedded flat surfaces in $\mathbb{H}^3$ with only one end and at most two isolated singularities.
This article is a continuation of a previous article which concerned the splitting problem for subspaces of superspaces. We begin with a general account of projective superspaces. Subsequently, we specialise to subvarieties of `positive'…
This short note summarizes the works done in collaboration between S. Belliard (CEA, Saclay), L. Frappat (LAPTh, Annecy), S. Pakuliak (JINR, Dubna), E. Ragoucy (LAPTh, Annecy), N. Slavnov (Steklov Math. Inst., Moscow) and more recently A.…
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods…
We obtain sharp estimates on the connectivity of complex affine hypersurfaces in terms of the decomposition of the defining equation as a sum of weighted homogeneous components relative to some weight system.
This is the third in a series of papers on the geometry and analysis of singular area minimizing hypersurfaces. We show how to derive obstruction and structure theories for scalar curvature constraints without imposing dimensional or…
We develop an algorithm computing the transcendental lattice and the Mordell--Weil group of an extremal elliptic surface. As an example, we compute the lattices of four exponentially large series of surfaces