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

  • Lattice Set
  • Convex Body
  • Projection
  • Grünbaum’s Inequality
  • Section
  • Congruent

• Graduation date

  Fall 2017

• 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.