The Topological Uniqueness of Complete One-ended Minimal Surfaces and Heegaard Surfaces in R Charles Frohman and William H. Meeks Iii

@inproceedings{Frohman1997TheTU,
title={The Topological Uniqueness of Complete One-ended Minimal Surfaces and Heegaard Surfaces in R Charles Frohman and William H. Meeks Iii},
author={Charles Frohman and William H. Meeks},
year={1997}
}

Theorem 1.1 was conjectured by Frohman [10] who proved it in the case that the surfaces are triply-periodic. Earlier Meeks [19] proved the theorem in the case of finite genus. In this case the only known examples are the plane, the helicoid and a recent example of Hoffman, Karcher and Wei [16]. However, the collection of properly embedded minimal surfaces of infinite genus and one end is extremely rich. One reason for this is that most classical examples of these surfaces are doublyperiodic (i… CONTINUE READING