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arXiv · 0910.0934

Some comments on spacelike minimal surfaces with null polygonal boundaries in $AdS_m$

Harald Dorn
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Abstract

We discuss some geometrical issues related to spacelike minimal surfaces in $AdS_m$ with null polygonal boundaries at conformal infinity. In particular for $AdS_4$, two holomorphic input functions for the Pohlmeyer reduced system are identified. This system contains two coupled differential equations for two functions $\alpha (z,\bar z)$ and $\beta (z,\bar z)$, related to curvature and torsion of the surface. Furthermore, we conjecture that, for a polynomial choice of the two holomorphic functions, the relative positions of their zeros encode the conformal invariant data of the boundary null $2n$-gon.

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Harald Dorn. 2009-10-06. Some comments on spacelike minimal surfaces with null polygonal boundaries in $AdS_m$. https://doi.org/10.1007/jhep02(2010)013

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