Related papers: Channel surfaces in Lie sphere geometry

We give a survey of the following six closely related topics: (i) a general method for constructing a soliton hierarchy from a splitting of a loop algebra into positive and negative subalgebras, together with a sequence of commuting…

We present dynamic equations for two dimensional closed surfaces and analytically solve it for some simplified cases. We derive final equations for surface normal motions by two different ways. The solution of the equations of motions in…

We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new two-parameter family of immersed helicoidal…

In this paper, we consider a method of constructing isothermic surfaces based on Ribaucour transformations. By applying the theory to the cylinder, we obtain a three-parameter family of complete isothermic surfaces that contains n-bubble…

In this article, we are concerned with various aspects of arcs on surfaces. In the first part, we deal with topological aspects of arcs and their complements. We use this understanding, in the second part, to construct interesting actions…

We give a geometric characterization of compact Riemann surfaces admitting orientation reversing involutions with fixed points. Such surfaces are generally called real surfaces and can be represented by real algebraic curves with non-empty…

We classify constant mean curvature surfaces invariant by a 1-parameter group of isometries in the Berger spheres and in the special linear group Sl(2, R). In particular, all constant mean curvature spheres in those spaces are described…

In this paper, we prove some convergence theorems for the mean curvature flow of closed submanifolds in the unit sphere $\mathbb{S}^{n+d}$ under integral curvature conditions. As a consequence, we obtain several differentiable sphere…

In this paper, we study Mannheim surface offsets in dual space. By the aid of the E. Study Mapping, we consider ruled surfaces as dual unit spherical curves and define the Mannheim offsets of the ruled surfaces by means of dual geodesic…

Let $\Lambda$ be the unit tangent bundle of the unit 3-sphere acted on transitively by the contact group of Lie sphere transformations. We study the Lie sphere geometry of generic curves in $\Lambda$ which are everywhere transversal to the…

The relation between differential geometry of surfaces and some Heisenberg ferromagnet models is considered.

Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.

This paper is devoted to a study of the connections between three different analytic descriptions for the immersion functions of 2D-surfaces corresponding to the following three types of symmetries: gauge symmetries of the linear spectral…

In Euclidean space we study surfaces with constant anisotropic mean curvature $\Lambda$ of the Dirichlet energy $\int_\Omega( |Du|^2+\Lambda u)$. We prove the existence of non-rotational surfaces with $\Lambda=0$ and foliated by a…

We study a transformation surface associated with a zero mean curvature surface in the three-dimensional Heisenberg group with respect to two left-invariant semi-Riemannian metrics. We investigate the duality and prove that the…

We review some geometric criteria and prove a refined version, that yield existence of capillary surfaces in tubes $\Omega\times \mathbb{R}$ in a gravity free environment, in the case of physical interest, that is, for bounded, open, and…

A space curve is determined by conformal arc-length, conformal curvature, and conformal torsion, up to M\"obius transformations. We use the spaces of osculating circles and spheres to give a conformally defined moving frame of a curve in…

The shape of a liquid surface bounded by an acute or obtuse planar angular sector is considered by using classical analysis methods. For acute angular sectors the two principal curvatures are of the order of the (fixed) mean curvature. But…

We show that some pieces of cylinders bounded by two parallel straight-lines bifurcate in a family of periodic non-rotational surfaces with constant mean curvature and with the same boundary conditions. These cylinders are initial…

We first note it is possible to construct two linear operators defined on two different domains, yet sharing the same spectrum using a geometric transform. However, one of these two operators will necessarily have spatially varying, matrix…