A Weierstrass type representation for translating solitons and singular minimal surfaces
نویسندگان
چکیده
In this paper we provide a Weierstrass representation formula for translating solitons and singular minimal surfaces in ${\mathbb{R}^3}$. As application study when the euclidean Gauss map has harmonic argument solve general Cauchy problem class of surfaces.
منابع مشابه
Weierstrass Representation of Periodic Minimal Surfaces
A general algorithm for the construction of infinite periodic minimal surfaces (IPMS) via their Weierstrass function is outlined, enabling parameterisation of known examples, and forming the bases of a systematic search for all such surfaces. For the 'regular' class of IPMS (including the low genus surfaces) the Weierstrass function has a simple form, permitting a complete listing of all possib...
متن کاملA Weierstrass Representation for Minimal Surfaces in 3-Dimensional Manifolds
In this paper we will discuss a Weierstrass type representation for minimal surfaces in Riemannian and Lorentzian 3-dimensional manifolds. Mathematics Subject Classification (2010). Primary 53C42; Secondary 53C50.
متن کاملWeierstrass Representation for Timelike Minimal Surfaces in Minkowski 3-space
Using techniques of integrable systems, we study a Weierstraß representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in Minkowski 3-space. The relationship between timelike minimal surfaces and bosonic Nambu-Goto ...
متن کاملA WEIERSTRASS TYPE REPRESENTATION FOR MINIMAL SURFACES IN SOL JUN-ICHI INOGUCHI AND SUNGWOOK LEE Dedicated to professor
The normal Gauss map of a minimal surface in the model space Sol of solvegeometry is a harmonic map with respect to a certain singular Riemannian metric on the extended complex plane.
متن کاملCanonical Weierstrass Representation of Minimal and Maximal Surfaces in the Three-dimensional Minkowski Space
We prove that any minimal (maximal) strongly regular surface in the threedimensional Minkowski space locally admits canonical principal parameters. Using this result, we find a canonical representation of minimal strongly regular time-like surfaces, which makes more precise the Weierstrass representation and shows more precisely the correspondence between these surfaces and holomorphic function...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2022
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2022.126528