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Reverse Isoperimetric Inequalities in R3

Gard, Andrew C.

Abstract Details

2012, Doctor of Philosophy, Ohio State University, Mathematics.
We formulate conditions under which the classical isoperimetric inequality in R3 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.
Fangyang Zheng, PhD (Advisor)
Bo Guan, PhD (Committee Member)
Ulrich Gerlach, PhD (Committee Member)
Christopher Hans, PhD (Committee Member)
57 p.

Recommended Citations

Citations

  • Gard, A. C. (2012). Reverse Isoperimetric Inequalities in R3 [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 R3. 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 R3." Doctoral dissertation, Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1330528578

    Chicago Manual of Style (17th edition)