Abstract/Details

Classification of stable minimal surfaces bounded by Jordan curves in close planes in Euclidean three-space


1998 1998

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Abstract (summary)

In this thesis we study compact stable embedded minimal surfaces whose boundary is given by two collections of closed smooth Jordan curves in two close parallel planes in Euclidean three-space.

Our main result is to give a classification of these minimal surfaces, under certain natural asymptotic geometric constraints, in terms of certain associated varifolds which can be enumerated explicitly.

One consequence of the main theorem is that under our hypotheses, there exists a unique area-minimizing surface, and this surface has the largest possible genus among all stable embedded minimal surfaces with boundary the two families of curves introduced above.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences, Close planes, Euclidean three-space, Jordan curves, Stable minimal surfaces
Title
Classification of stable minimal surfaces bounded by Jordan curves in close planes in Euclidean three-space
Author
Galotta, Rosanna
Number of pages
52
Publication year
1998
Degree date
1998
School code
0118
Source
DAI-B 59/10, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780599073272, 0599073276
Advisor
Meeks, William H., III
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9909165
ProQuest document ID
304437963
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304437963
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