Tohoku Mathematical Journal
2001

June
SECOND SERIES VOL. 53, NO. 2

Tohoku Math. J.
53 (2001), 305-318

Title SURFACES OF CONSTANT MEAN CURVATURE ONE IN THE HYPERBOLIC THREE-SPACE WITH IRREGULAR ENDS

Author Zuhuan Yu

(Received August 4, 1999, revised September 21, 2000)
Abstract. We investigate surfaces of constant mean curvature one in the hyperbolic three-space with irregular ends, and prove that their irregular ends must self-intersect, which answers affirmatively a conjecture of Umehara and Yamada. Moreover we also obtain an explicit representation of a constant mean curvature one surface and a new minimal surface in the Euclidean three-space.

2000 Mathematics Subject Classification. Primary 53A35; Secondary 53B20.

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