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In this article, we continue to study the geometry of bisections of certain rational elliptic surfaces. As an application, we give examples of Zariski N + 1-plets of degree 2N + 4 whose irreducible components are an irreducible quartic…
End sum is a natural operation for combining two noncompact manifolds and has been used to construct various manifolds with interesting properties. The uniqueness of end sum has been well-studied in dimensions three and higher. We study end…
In this note, we study the infinitesimal forms of Deligne cycle class maps. As an application, we prove that the infinitesimal form of a conjecture by Beilinson is true.
In this paper we obtain a bound on the number of isometry classes of finite area hyperbolic surfaces which are length isospectral to a given surface depending only on the topological type of the surface and the length of the shortest closed…
Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary…
We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical…
We propose a novel way of computing surface folding maps via solving a linear PDE. This framework is a generalization to the existing quasiconformal methods and allows manipulation of the geometry of folding. Moreover, the crucial quantity…
Solutions to the Dirac equation are obtained by considering functions of axial type. This indeed gives rise to Vekua systems that can be solved in terms of special functions. In this paper we investigate axial symmetry for the solutions of…
We study the inverse resonance problem for conformally compact manifolds which are hyperbolic outside a compact set. Our results include compactness of isoresonant metrics in dimension two and of isophasal negatively curved metrics in…
In this paper, we determine the asymptotic dimension for all surface braid groups -- including those associated with non-orientable and infinite-type surfaces -- as well as for torsion-free poly-finitely generated surface groups. We…
The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the nontriviality of certain cycles of…
In this paper we construct a class of infinite-dimensional Frobenius manifolds in the spaces of pairs of meromorphic functions defined on certain regions of the Riemann sphere. For such Frobenius manifolds, we obtain their principal…
In the article it was shown the convergence of special integral of two dimensional Terry's problem. Main tools of the article are an investigation of real algebraic varieties and estimations of areas of algebraic surfaces.
The study of graph drawings on 2-surfaces is an active area of mathematical research. Our main results are criteria for integer and modulo 2 embeddability of graphs to surfaces.
In this paper, we describe an elementary method for counting the number of non-isomorphic algebras of a fixed dimension over a given finite field. We show how this method works for the explicit example of $2$-dimensional algebras over the…
We consider versal deformations of 0|3-dimensional L-infinity algebras, which correspond precisely to ordinary (non-graded) three dimensional Lie algebras. The classification of such algebras over C is well known, although we shall give a…
In this paper, we will establish a general method of studying finite-dimensional normed spaces, and apply this method to classifying $3$-dimensional and $4$-dimensional normed spaces over a non-spherically complete field. For this purpose,…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe…
We solve, numerically, the massless spin-2 equations, written in terms of a gauge based on the properties of conformal geodesics, in a neighbourhood of spatial infinity using spectral methods in both space and time. This strategy allows us…