The Erwin Schr odinger International Boltzmanngasse
ESI Institute for Mathematical Physics A Wien Austria
A Weierstrass Representation
Theorem for Lorentz Surfaces
Jerzy Julian Konderak
Vienna Preprint ESI Octob er
Supp orted by Federal Ministry of Science and Transp ort Austria
Available via http www esi ac at
A WEIERSTRASS REPRESENTATION
THEOREM FOR LORENTZ SURFACES
Jerzy Julian KONDERAK
Octob er
Abstract
We consider functions with values in the algebra of Lorentz num
b ers L and which are di erentiable with resp ect to the algebraic struc
ture of this algebra L as an analogue of the holomorphic functions
Then we apply this functions to prove a Weierstrass representation
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theorem for Lorentz surfaces immersed in the space R In the pro of
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we essentially follow the mo del of the complex numb ers We apply
our representation theorem to construct explicit minimal immersions