Off-campus UMass Amherst users: To download dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users, please click the view more button below to purchase a copy of this dissertation from Proquest.
(Some titles may also be available free of charge in our Open Access Dissertation Collection, so please check there first.)
Desingularizing the intersection between a catenoid and a plane
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. ^
"Desingularizing the intersection between a catenoid and a plane"
(January 1, 1997).
Doctoral Dissertations Available from Proquest.