Completing the conformal boundary of a simply connected Lorentz surface

Smyth, Robert

doi:10.1090/S0002-9939-01-06067-1

Completing the conformal boundary of a simply connected Lorentz surface
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Proc. Amer. Math. Soc. 130 (2002), 841-847 Request permission

Abstract:

This paper extends Kulkarni’s conformal boundary $\partial {\mathcal {L}}$ for a simply connected Lorentz surface $\mathcal {L}$ to a compact conformal boundary $\partial ^c\mathcal {L}$. The procedure used is analogous to Carathéodory’s construction (in the definite metric setting) of prime ends from the accessible points of a bounded simply connected planar domain. The space $\partial ^c\mathcal {L}$ of conformal boundary elements is homeomorphic to the circle, and contains Kulkarni’s conformal boundary $\partial {\mathcal {L}}$ as a dense subspace.

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