Thesis (MSc)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.

Lee, King Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leave 95). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Organization --- p.10 / Chapter 2 --- Semigroups and Cones --- p.13 / Chapter 2.1 --- Relation between Semigroups and Cones --- p.13 / Chapter 2.2 --- Subadditive Functions on Semigroups --- p.23 / Chapter 2.3 --- Relation between Cones and Bases --- p.29 / Chapter 3 --- General Theories of Okounkov Bodies --- p.33 / Chapter 3.1 --- Okounkov Bodies and Volumes --- p.33 / Chapter 3.2 --- Relation of Subadditive Functions on Semigroups and Okounkov Bodies --- p.39 / Chapter 3.3 --- Convex Functions on Okounkov Bodies --- p.47 / Chapter 4 --- Okounkov Bodies and Complex Geometry --- p.55 / Chapter 4.1 --- Holomorphic Line Bundles --- p.55 / Chapter 4.2 --- Chebyshev Transform --- p.65 / Chapter 4.3 --- Bernstein-Markov Norms --- p.74 / Chapter 5 --- Applications of Okounkov Bodies --- p.81 / Chapter 5.1 --- Relative Energy of Weights --- p.81 / Chapter 5.2 --- Computational Methods and Some Examples --- p.89 / Bibliography --- p.95

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Diss. (sammanfattning) Uppsala : Univ., 2004. / Härtill 4 uppsatser.

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Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (March 1, 2007) Vita. Includes bibliographical references.

Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (March 1, 2007) Vita. Includes bibliographical references.

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2005. / Includes bibliographical references (p. 51).

In this thesis we study Mahler's conjecture in convex geometry, give a short summary about its history, gather and explain different approaches that have been used to attack the conjecture, deduce formulas to calculate the Mahler volume and perform numerical analysis on it. The conjecture states that the Mahler volume of any symmetric convex body, i.e. the product of the volume of the symmetric convex body and the volume of its dual body, is minimized by the (hyper-)cube. The conjecture was stated and solved in 1938 for the 2-dimensional case by Kurt Mahler. While the maximizer for this problem is known (it is the ball), the conjecture about the minimizer is still open for all dimensions greater than 2. A lot of effort has benn made to solve this conjecture, and many different ways to attack the conjecture, from simple geometric attempts to ones using sophisticated results from functional analysis, have all been tried unsuccesfully. We will present and discuss the most important approaches. Given the support function of the body, we will then introduce several formulas for the volume of the dual and the original body and hence for the Mahler volume. These formulas are tested for their effectiveness and used to perform numerical work on the conjecture. We examine the conjectured minimizers of the Mahler volume by approximating them in different ways. First the spherical harmonic expansion of their support functions is calculated and then the bodies are analyzed with respect to the length of that expansion. Afterwards the cube is further examined by approximating its principal radii of curvature functions, which involve Dirac delta functions.