Show simple item record

dc.contributor.authorWhite, Edward C., Jr.en_US
dc.date.accessioned2008-09-17T19:29:59Z
dc.date.available2008-09-17T19:29:59Z
dc.date.issued2008-07-10en_US
dc.identifier.urihttp://hdl.handle.net/1853/24689
dc.description.abstractThis thesis examines the elegant theory of polar and Legendre duality, and its potential use in convex geometry and geometric analysis. It derives a theorem of polar - Legendre duality for all convex bodies, which is captured in a commutative diagram. A geometric flow on a convex body induces a distortion on its polar dual. In general these distortions are not flows defined by local curvature, but in two dimensions they do have similarities to the inverse flows on the original convex bodies. These ideas can be extended to higher dimensions. Polar - Legendre duality can also be used to examine Mahler's Conjecture in convex geometry. The theory presents new insight on the resolved two-dimensional problem, and presents some ideas on new approaches to the still open three dimensional problem.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectDualityen_US
dc.subjectConvex geometryen_US
dc.subjectGeometric flowsen_US
dc.subjectGeometric analysisen_US
dc.subject.lcshConvex geometry
dc.subject.lcshFluid dynamic measurements
dc.subject.lcshLegendre's functions
dc.subject.lcshCoordinates, Polar
dc.subject.lcshDuality theory (Mathematics)
dc.subject.lcshDifferential equations
dc.titlePolar - legendre duality in convex geometry and geometric flowsen_US
dc.typeThesisen_US
dc.description.degreeM.S.en_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Evans Harrell; Committee Member: Guillermo Goldsztein; Committee Member: Mohammad Ghomien_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record