Proceedings of the American Mathematical Society

Author(s): Robert W. Smyth
Journal: Proc. Amer. Math. Soc. 130 (2002), 841-847.
MSC (2000): Primary 53C50, 53A30
Posted: August 29, 2001
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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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