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osu1330528578.pdf (608.82 KB)
ETD Abstract Container
Abstract Header
Reverse Isoperimetric Inequalities in R
3
Author Info
Gard, Andrew C.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1330528578
Abstract Details
Year and Degree
2012, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
We formulate conditions under which the classical isoperimetric inequality in R
3
can be reversed. Restricting our attention to surfaces with rotational symmetry, we enforce bounds on curvature and overall size (both in the appropriate technical senses) and show that these suffice to guarantee the existence of shapes of minimal volume for given fixed surface area. In the fundamental case where both principal curvatures are bounded, we construct the surface of minimal volume.
Committee
Fangyang Zheng, PhD (Advisor)
Bo Guan, PhD (Committee Member)
Ulrich Gerlach, PhD (Committee Member)
Christopher Hans, PhD (Committee Member)
Pages
57 p.
Subject Headings
Mathematics
Keywords
reverse isoperimetric
;
reverse inequality
;
andy gard
;
andrew gard
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Citations
Gard, A. C. (2012).
Reverse Isoperimetric Inequalities in R
3
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1330528578
APA Style (7th edition)
Gard, Andrew.
Reverse Isoperimetric Inequalities in R
3
.
2012. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1330528578.
MLA Style (8th edition)
Gard, Andrew. "Reverse Isoperimetric Inequalities in R
3
." Doctoral dissertation, Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1330528578
Chicago Manual of Style (17th edition)
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Document number:
osu1330528578
Download Count:
576
Copyright Info
© 2012, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.