Abstract/Details

Isoperimetric inequalities and concave functions


1999 1999

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Abstract (summary)

In this thesis we prove a one parameter family of Bonnesen-style and Osserman-style discrete Sobolev inequalities which hold for a large class of concave functions. We will show that this class of concave functions include solutions of some well known second order differential equations. In particular, for the sine and cosine functions we will apply these discrete Sobolev inequalities to obtain uncountably many new Bonnesen-style and Osserman-style isoperimetric inequalities for the generalized star polygon Pn,m of type {[special characters omitted]}. We will also see that for certain classes of polygons P n we are able to give a complete solution for the existence of Bonnesen-style and Osserman-style isoperimetric inequalities. Our inequalities will be extended further to include the surfaces of constant curvature and prove global Bonnesen-style and Osserman-style inequalities for the generalized star polygon on the unit 2-sphere, hyperbolic plane and Euclidean plane. Finally, derived from the geometry of the surface, we develop Hyperbolic and Elliptic lengths and areas to prove additional interesting inequalities on the unit 2-sphere and hyperbolic plane.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Bonnesen inequalities; Concave functions; Isoperimetric inequalities; Osserman inequalities
Title
Isoperimetric inequalities and concave functions
Author
Ferland, Alane Susan
Number of pages
73
Publication year
1999
Degree date
1999
School code
0118
Source
DAI-B 60/05, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780599328839, 0599328835
Advisor
Ku, Mei-Chin
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
9932309
ProQuest document ID
304536298
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304536298
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