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Bounds on packing density via slicing

Kusner, Wöden (2014) Bounds on packing density via slicing. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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This document is composed of a series of articles in discrete geometry, each solving a problem in packing density.

• The first proves a local upper bound for the packing density of regular pentagons in R2. By reducing a nonlinear programming problem to a linear one, computational methods show that the conjectured global optimal solution is locally optimal.

• The second proves an upper bound for the packing density of finite cylinders in R3. Using a measure theoretic approach to estimate boundary error, the first bound that is asymptotically sharp with respect to the length of the cylinder is found. This gives the first sharp upper bound for the packing density of half-infinite cylinders as a corollary.

• The third proves an upper bound for the packing density of infinite polycylinders in Rn. Using transversality and a dimension reduction argument, an existing result for R3 is applied to Rn. This gives the first non-trivial sharp upper bound for the packing density of any object in dimensions four and greater.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Kusner, Wö
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairHales, Thomashales@pitt.eduHALES
Committee MemberConstantine, Gregorygmc@pitt.eduGMC
Committee MemberJiang, Huiqianghqjiang@pitt.eduHQJIANG
Committee MemberDeBlois, Jasonjdeblois@pitt.eduJDEBLOIS
Committee MemberRollett,
Date: 23 September 2014
Date Type: Publication
Defense Date: 22 May 2014
Approval Date: 23 September 2014
Submission Date: 22 May 2014
Access Restriction: 1 year -- Restrict access to University of Pittsburgh for a period of 1 year.
Number of Pages: 77
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: MSC2010[52C17] (packing in n dimensions), MSC2010[05B40] (packing and covering), MSC2010[11H31] (lattice packing and covering), discrete geometry, nonlinear programming, conical programming, interval arithmetic, measure theory, foliations, slicing
Date Deposited: 23 Sep 2014 18:32
Last Modified: 15 Nov 2016 14:20


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