arXiv subjects
Publications and source records attributed to W. Rossman.
Using discretized orthogonal systems (curvature line systems) with periodicity, created using Darboux transformations and their permutability, we have discrete and semi-discrete k-dimensional isothermic tori which are full in n-dimensional Euclidean space, for any natural numbers k between 2 nd n.
We provide a convincing discretisation of Demoulin's $Ω$-surfaces along with their specialisations to Guichard and isothermic surfaces with no loss of integrable structure.
Discrete linear Weingarten surfaces in space forms are characterized as special discrete $Ω$-nets, a discrete analogue of Demoulin's $Ω$-surfaces. It is shown that the Lie-geometric deformation of $Ω$-nets descends to a Lawson transformation for discrete linear Weingarten surfaces, which coincides with the well-known Lawson correspondence in the constant mean curvature case.
A Darboux transformation for polarized space curves is introduced and its properties are studied, in particular, Bianchi permutability. Semi-discrete isothermic surfaces are described as sequences of Darboux transforms of polarized curves in the conformal n-sphere and their transformation theory is studied. Semi-discrete surfaces of constant mean curvature are studied as an application of the transformation theory.
The generalized Weierstrass representation is used to analyze the asymptotic behavior of a constant mean curvature surface that arises locally from an ordinary differential equation with a regular singularity. We prove that a holomorphic perturbation of an ODE that represents a Delaunay surface generates a constant mean curvature surface which has a properly immersed end that is asymptotically Delaunay. Furthermore, that end is embedded if the Delaunay surface is unduloidal.