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Reverse Isoperimetric Inequalities in R3
Gard, Andrew C.

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.

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Gard, A. (2012). Reverse Isoperimetric Inequalities in R3. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Gard, Andrew. "Reverse Isoperimetric Inequalities in R3." Electronic Thesis or Dissertation. Ohio State University, 2012. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Gard, Andrew "Reverse Isoperimetric Inequalities in R3." Electronic Thesis or Dissertation. Ohio State University, 2012. https://etd.ohiolink.edu/

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