Ruled minimal surfaces in ℝ³ with density e^z

Doan The Hieu and Nguyen Minh Hoang

Vol. 243 (2009), No. 2, 277–285

DOI: 10.2140/pjm.2009.243.277

Abstract

We classify ruled minimal surfaces in ℝ³ with density e^z. We show that there is a family of cylindrical ones and that there are no others. Also, all translation minimal surfaces are ruled.

Keywords

log-linear density, ruled minimal surfaces, translation minimal surfaces

Mathematical Subject Classification 2000

Primary: 53C25

Secondary: 53A10, 49Q05

Milestones

Received: 10 February 2009

Revised: 23 March 2009

Accepted: 27 March 2009

Published: 1 December 2009