Related papers: Hill's level surfaces in the circular restricted t…
We study surfaces of constant positive Gauss curvature in Euclidean 3-space via the harmonicity of the Gauss map. Using the loop group representation, we solve the regular and the singular geometric Cauchy problems for these surfaces, and…
In the restricted three-body problem, consecutive collision orbits are those orbits which start and end at collisions with one of the primaries. Interests for such orbits arise not only from mathematics but also from various engineering…
This article reports the spherical coordinate form of three-dimensional generalized dynamics of soft-matter quasicrystals with 12-fold symmetry which provides a basis for solving initial-boundary value problems of the equations under some…
In this paper, helicoidal flat surfaces in the $3$-dimensional sphere $\mathbb{S}^3$ are considered. A complete classification of such surfaces is given in terms of their first and second fundamental forms and by linear solutions of the…
This note contains a solution to the following problem: reconstruct the definition field and the equation of a projective cubic surface, using only combinatorial information about the set of its rational points. This information is encoded…
This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines the stabilized trace finite element method for spatial…
An exact rotating anisotropic fluid solution and a family of exact rotating anisotropic fluid solutions are presented which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor the…
The problem of optimization of a cycle of tangential deformations of the surface of a spherical object (microsquirmer) self-propelling in a viscous fluid at low Reynolds numbers is represented in a noncanonical Hamiltonian form. The…
On a real regular elliptic surface without multiple fiber, the Betti number $h_1$ and the Hodge number $h^{1,1}$ are related by $h_1\leq h^{1,1}$. We prove that it's always possible to deform such algebraic surface to obtain $h_1=h^{1,1}$.…
For three-body problem, R.Montgomery [3] proved a reconstruction formula which calculates the overall rotation relating two similar triangle configurations if the initial triangular configuration is similar to the configuration formed at…
We give a fast, exact algorithm for solving Dirichlet problems with polynomial boundary functions on quadratic surfaces in R^n such as ellipsoids, elliptic cylinders, and paraboloids. To produce this algorithm, first we show that every…
We study almost complex surfaces in the nearly K\"ahler $S^3\times S^3$. We show that there is a local correspondence between almost complex surfaces and solutions of the H-surface equation introduced by Wente. We find a global holomorphic…
Associated to every complete affine 3-manifold M with nonsolvable fundamental group is a noncompact hyperbolic surface S. We classify such complete affine structures when Sigma is homeomorphic to a three-holed sphere. In particular, for…
Explicit solutions of the two-dimensional floating body problem (bodies that can float in all positions) for relative density rho different from 1/2 and of the tire track problem (tire tracks of a bicycle, which do not allow to determine,…
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…
We define hyperbolic Heron triangles (hyperbolic triangles with "rational" side-lengths and area) and parametrize them in two ways as rational points of certain elliptic curves. We show that there are infinitely many hyperbolic Heron…
It is shown that analytic conformal submersions of $S^3$ are given by intersections of (not necessary closed) complex surfaces with a quadratic real hyper-surface in $\mathbb{C}P^3.$ A new description of the space of circles in the 3-sphere…
A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (``acceleration equal force'') equations of motion, featuring one-body (``external'') and pair (``interparticle'') forces. The…
The large distance behavior of weakly bound three-body systems is investigated. The Schr\"{o}dinger equation and the Faddeev equations are reformulated by an expansion in eigenfunctions of the angular part of a corresponding operator. The…
Spherically and cylindrically symmetric solutions of SU(3) Yang-Mills theory are found, whose gauge potentials have confining properties. The spherically symmetric solutions give field distributions which have a spherical surface on which…