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Desingularizing the intersection between a catenoid and a plane

Haiping Luo, University of Massachusetts - Amherst

Abstract

The main result of this thesis states that given the union X of a vertical catenoid and a fixed horizontal plane, then there exists a sequence of the Hoffman-Meeks-Karcher minimal surfaces (properly normalized) that converges to X. We also prove that a subsequence of these surfaces, when properly normalized, converge to a Scherk singly-period minimal surface whose angle is the same as the angle between the catenoid and the plane.^ Another result in this thesis is the uniqueness of the genus-one Scherk singly-periodic minimal surface. This result gives a classification of the genus-1 singly-periodic properly embedded minimal surfaces with four Scherk-type ends. We also generalize this result to 2n Scherk-type ends. ^

Subject Area

Mathematics

Recommended Citation

Haiping Luo, "Desingularizing the intersection between a catenoid and a plane" (January 1, 1997). Doctoral Dissertations Available from Proquest. Paper AAI9809361.
http://scholarworks.umass.edu/dissertations/AAI9809361

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