Results 1 to 10 of about 433 (137)

Weierstrass-type representations [PDF]

Geometriae Dedicata, 2019
Weierstrass-type representations have been used extensively in surface theory to create surfaces with special curvature properties. In this paper we give a unified description of these representations in terms of classical transformation theory of $Ω$-surfaces.
Mason Pember, Pember Mason
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The Weierstrass—Enneper representation using hodographic coordinates on a minimal surface [PDF]

Proceedings Mathematical Sciences, 2003
In this paper we obtain the general solution to the minimal surface equation, namely its local Weierstrass-Enneper representation, by using a system of hodographic coordinates. This is done by using the method of solving the Born-Infeld equations by Whitham.
Dey Rukmini
openaire   +4 more sources

Generalized Weierstrass representation for surfaces in multi-dimensional Riemann spaces [PDF]

Journal of Geometry and Physics, 1999
LaTeX, 20 pages, minor misprints ...
KONOPELCHENKO, Boris, LANDOLFI, Giulio
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Representation of cyclic groups in positive characteristic and Weierstrass semigroups

Journal of Number Theory, 2013
15 ...
Karanikolopoulos, S., Kontogeorgis, A.
openaire   +5 more sources

Discrete Weierstrass-Type Representations [PDF]

Discrete & Computational Geometry, 2022
22 pages, 4 ...
Mason Pember, Denis Polly, Masashi Yasumoto   +2 more
openaire   +2 more sources

Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering

Mathematics, 2021
In this work, we study the generalized 2D equal-width equation which arises in various fields of science. With the aid of numerous methods which includes Lie symmetry analysis, power series expansion and Weierstrass method, we produce closed-form ...
Chaudry Masood Khalique, Karabo Plaatjie
doaj   +1 more source

Appell and Sheffer sequences: on their characterizations through functionals and examples

Comptes Rendus. Mathématique, 2021
The aim of this paper is to present a new simple recurrence for Appell and Sheffer sequences in terms of the linear functional that defines them, and to explain how this is equivalent to several well-known characterizations appearing in the literature ...
Carrillo, Sergio A., Hurtado, Miguel
doaj   +1 more source

On multivortex solutions of the weierstrass representation [PDF]

Physics of Atomic Nuclei, 2002
The connection between the complex Sine and Sinh-Gordon equations on the complex plane associated with a Weierstrass type system and the possibility of construction of several classes of multivortex solutions is discussed in detail. We perform the Painlevé test and analyse the possibility of deriving the Bäcklund transformation from the singularity ...
Bracken, P., Goldstein, P. P., Grundland, A. M.   +2 more
openaire   +2 more sources

Minimal surfaces with non-trivial geometry in the three-dimensional Heisenberg group

Complex Manifolds, 2022
We study symmetric minimal surfaces in the three-dimensional Heisenberg group Nil3 using the generalized Weierstrass type representation, the so-called loop group method.
Dorfmeister Josef F., Inoguchi Jun-ichi, Kobayashi Shimpei   +2 more
doaj   +1 more source

The Algebraic Surfaces of the Enneper Family of Maximal Surfaces in Three Dimensional Minkowski Space

Axioms, 2021
We consider the Enneper family of real maximal surfaces via Weierstrass data (1,ζm) for ζ∈C, m∈Z≥1. We obtain the irreducible surfaces of the family in the three dimensional Minkowski space E2,1.
Erhan Güler
doaj   +1 more source