Canonical Weierstrass representations are obtained for maximal space-like surfaces in R^4_2, solving the natural PDE system explicitly with pairs of holomorphic functions and linking them to maximal surfaces in 3D Minkowski space.
Canonical Weierstrass Representation of Minimal and Maximal Surfaces in the Three-dimensional Minkowski Space
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abstract
We prove that any minimal (maximal) strongly regular surface in the three-dimensional 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 functions (in the Gauss plane). We also find a canonical representation of maximal strongly regular space-like surfaces, which makes more precise the Weierstrass representation and shows more precisely the correspondence between these surfaces and holomorphic functions (in the Lorentz plane). This allows us to describe locally the solutions of the corresponding natural partial differential equations.
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math.DG 1years
2019 1verdicts
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Canonical Weierstrass Representations for Maximal Space-like Surfaces in $\RR^4_2$
Canonical Weierstrass representations are obtained for maximal space-like surfaces in R^4_2, solving the natural PDE system explicitly with pairs of holomorphic functions and linking them to maximal surfaces in 3D Minkowski space.