Weierstrass-Enneper representation for Maximal Surfaces in Hodographic coordinates
Rahul Kumar Singh
TL;DR
This paper derives a Weierstrass-Enneper representation for maximal surfaces in Lorentz-Minkowski space using a method related to the Born-Infeld equation, revealing a connection via Wick rotation.
Contribution
It introduces a novel representation for maximal surfaces in Lorentz-Minkowski space by linking it to the Born-Infeld equation through hodographic coordinates.
Findings
Derived the Weierstrass-Enneper representation for maximal graphs
Established a connection between maximal surface equations and Born-Infeld equation
Applied hodographic coordinates to relate different geometric equations
Abstract
We obtain the Weierstrass-Enneper representation for maximal graphs(whose Gauss map is one-one) in Lorentz-Minkowski space. For this we use the method of Barbishov and Chernikov, which they have used to find the solutions of Born-Infeld equation in hodographic coordinates. We could use their method in our case, because we realized that the maximal surface equation and Born-Infeld equation are related via a wick rotation in the first variable of the parametrising domain.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Scientific Research and Discoveries · 3D Shape Modeling and Analysis