Discrete Energy on Rectifiable Sets

Discrete Energy on Rectifiable Sets by Sergiy V. Borodachov, Douglas P. Hardin, Edward B. Saff.

This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations. Written by leading authorities on the topic, this treatise is designed with the graduate student and further explorers in mind. The presentation includes a chapter of prel...

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Bibliographic Details
Main Authors: Borodachov, Sergiy V. (Author), Hardin, Douglas P. (Author), Saff, Edward B. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2019.
Edition:1st ed. 2019.
Series:Springer Monographs in Mathematics,
Springer eBook Collection.
Subjects:
Convex geometry .
Discrete geometry.
Physics.
Measure theory.
Number theory.
Topology.
Information theory.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 0. An Overview: Discretizing Manifolds via Particle Interactions.-1. Preliminaries
  • 2. Basics of Minimal Energy
  • 3.-Introduction to Packing and Covering
  • 4. Continuous and Discrete Energy
  • 5. LP Bounds on the Sphere
  • 6. Asymptotics for Energy Minimizing Congurations on Sd
  • 7. Some Popular Algorithms for Distributing Points on S2
  • 8. Minimal Energy in the Hypersingular Case
  • 9. Minimal Energy Asymptotics in the "Harmonic Series" Case
  • 10. Periodic Riesz Energy
  • 11. Congurations with non-Uniform Distribution
  • 12. Low Complexity Energy Methods for Discretization
  • 13. Best-Packing on Compact Sets
  • 14. Optimal Discrete Measures for Potentials: Polarization (Chebyshev) Constants
  • Appendix
  • References
  • List of Symbols
  • Index.

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