Abstract
The Convex Body Isoperimetric Conjecture states that the least perimeter needed to enclose a volume within a ball is greater than the least perimeter needed to enclose the same volume within any other convex body of the same volume in Rn. We focus on the conjecture in the plane and prove a new sharp lower bound for the isoperimetric profile of the disk in this case. We prove the conjecture in the case of regular polygons, and show that in a general planar convex body the conjecture holds for small areas.
Author Bio
John Berry was an undergraduate student at Williams College.
Eliot Bongiovanni is an undergraduate student at Michigan State University majoring in advanced mathematics and statistics. He plans to pursue a PhD in geometric analysis. When he is not doing mathematics, he can often be found producing and hosting his metal radio program.
Wyatt Boyer was an undergraduate student at Williams College.
Brian Brown was an undergraduate student at Pomona College.
Matthew Dannenberg was an undergraduate student at Harvey Mudd College.
Paul Gallagher was an undergraduate student at the University of Pennsylvania.
David Hu was an undergraduate student at Georgetown University.
Jason Liang was an undergraduate student at the University of Chicago.
Alyssa Loving was an undergraduate student at the University of Hawaii.
Zane Martin was an undergraduate student at Williams College.
Maggie Miller was an undergraduate at UT Austin during this project. She is currently a graduate student in the math department at Princeton, where she is interested in geometric topology. She has a large collection of Rubik's cubes and similar toys, and enjoys solving crossword puzzles.
Byron Perpetua was an undergraduate student at Williams College.
Sarah Tammen is a 2016 graduate of the University of Georgia, where she earned a bachelor’s degree in mathematics. She participated in the SMALL REU in the summer of 2014. She is presently pursuing a PhD in mathematics at the Massachusetts Institute of Technology.
Yingyi Zeng was an undergraduate student at St. Mary’s College of Maryland.
Recommended Citation
Berry, John; Bongiovanni, Eliot; Boyer, Wyatt; Brown, Bryan; Gallagher, Paul; Hu, David; Loving, Alyssa; Martin, Zane; Miller, Maggie; Perpetua, Byron; and Tammen, Sarah
(2017)
"The Convex Body Isoperimetric Conjecture in the Plane,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 18:
Iss.
2, Article 2.
Available at:
https://scholar.rose-hulman.edu/rhumj/vol18/iss2/2
