Discrete Energy on Rectifiable Sets

• Main Authors: Borodachov, Sergiy V. (Author, http://id.loc.gov/vocabulary/relators/aut), Hardin, Douglas P. (http://id.loc.gov/vocabulary/relators/aut), Saff, Edward B. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Springer Monographs in Mathematics,
• Subjects: Convex geometry .; Discrete geometry.; Physics.; Measure theory.; Number theory.; Topology.; Information theory.; Convex and Discrete Geometry.; Mathematical Methods in Physics.; Measure and Integration.; Number Theory.; Information and Communication, Circuits.

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...

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.