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Topics in Convex Geometric Analysis and Discrete Tomography

  • Author / Creator
    Zhang, Ning
  • In this thesis, some topics in convex geometric analysis and discrete tomography are studied. Firstly, let K be a convex body in the n-dimensional Euclidean space. Is K uniquely determined by its sections? There are classical results that explain what happens in the case of sections passing through the origin. However, much less is known about sections that do not contain the origin. Here, several problems of this type and the corresponding uniqueness results are established. We also establish a discrete analogue of the Aleksandrov theorem for the areas and the surface areas of projections. Finally, we find the best constant for the Grünbaum’s inequality for projections, which generalizes both Grünbaum’s inequality, and an old inequality of Minkowski and Radon.

  • Subjects / Keywords
  • Graduation date
    2017-11
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R38G8FX53
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Vladyslav Yaskin
  • Examining committee members and their departments
    • Litvak, Alexander (Mathematical and Statistical Sciences)
    • Stancu, Alina (Mathematics and Statistics, Concordia University )
    • Yaskin, Vladyslav (Mathematical and Statistical Sciences)
    • Dai, Feng (Mathematical and Statistical Sciences)
    • Troitsky, Vladimir (Mathematical and Statistical Sciences)
    • Yu, Xinwei (Mathematical and Statistical Sciences)