We describe infinitesimal deformations of constant mean curvature surfaces of finite type in the 3-sphere. We use Baker-Akhiezer functions to describe such deformations, as well as polynomial Killing fields and the corresponding spectral curve to distinguish between isospectral and non-isospectral deformations.

∂-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy * B. Konopelchenko Abstract It is shown that the dispersionless scalar integrable hierarchies and, in general, the universal Whitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane. Examples of deformations of quasiconformal mappings associated with explicit...

Non-classical, "structured deformations" are used to describe microslip and to refine both balance laws and constitutive relations. The main tools employed are identification relations that link the ingredients in structui'ed deformations to geometrical changes at small length scales. Short title: Structured Deformations and Microslip Telephone: (412) 268-8481 Fax: (412) 268-6380 E-mail: do04@a...

A previously introduced scheme for describing integrable deformations of of algebraic curves is completed. Lenard relations are used to characterize and classify these deformations in terms of hydrodynamic type systems. A general solution of the compatibility conditions for consistent deformations is given and expressions for the solutions of the corresponding Lenard relations are provided.

Induced surfaces and their integrable dynamics. II. Generalized Weierstrass representations in 4D spaces and deformations via DS hierarchy. Abstract Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfa...

The effect of plastic deformation on the grain boundary surface area per unit volume and edge length per unit volume is examined using two methods. The first by applying homogeneous deformations to tetrakaidecahedra in a variety of orientations and the second by using the principles of stereology. It is shown that the methods produce essentially identical results. It is now possible to calculat...

— We prove that the dimension of the deformations of a given generic Fuchsian system without changing the conjugacy class of its local monodromies (“number of accessory parameters”) is equal to half the dimension of the moduli space of deformations of the associated local system. We do this by constructing a weight 1 Hodge structure on the infinitesimal deformations of integrable connections. W...

This paper suveys some recent algebraic developments in two parameter Quantum deformations and their Nonstandard (or Jordanian) counterparts. In particular, we discuss the contraction procedure and the quantum group homomorphisms associated to these deformations. The scheme is then set in the wider context of the coloured extensions of these deformations, namely, the so-called Coloured Quantum ...

In this paper we develop the theory of equisingular deformations of plane curve singularities in arbitrary characteristic. We study equisingular deformations of the parametrization and of the equation and show that the base space of its semiuniveral deformation is smooth in both cases. Our approach through deformations of the parametrization is elementary and we show that equisingular deformati...

In anatomical illustrations deformation is often used to increase expressivity, to improve spatial comprehension and to enable an unobstructed view onto otherwise occluded structures. Based on our analysis and classification of deformations frequently found in anatomical textbooks we introduce a technique for interactively creating such deformations of volumetric data acquired with medical scan...