Mystery of point charges

Proceedings of the London Mathematical Society

Volumn 95, Issue 2, 2007, Pages 443-472

  Gabrielov, A ^a   Novikov, D ^b   Shapiro, B ^c  

^a PURDUE UNIVERSITY   (United States)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^c STOCKHOLM UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 47149113486     PISSN: 00246115     EISSN: 1460244X     Source Type: Journal    
DOI: 10.1112/plms/pdm012     Document Type: Article

References (20)

1. A. A. Agrachev, D. Pallaschke and S. Scholtes, 'On Morse theory for piecewise smooth functions', J. Dynam. Control Systems 3 (1997) 449-469.
2. D. N. Bernstein, 'The number of roots of a system of equations', Funktsional. Anal. i Priložen. 9 (1975) no.3, 1-4.
3. H. Edelsbrunner, Algorithms in combinatorial geometry (Springer, Berlin, 1987).
4. C. F. Gauss, Collected works, 1st edn (Teubner, Leipzig, 1870-1917) vol.3, p. 112; vol.8, p. 32; vol.10, part 2, pp. 189-191.
5. J. E. Goodman and J. O'Rourke (eds), Handbook of discrete and computational geometry (CRC Press, Boca Raton, FL, 1997).
6. A. A. Janušauskas, 'Critical points of electrostatic potentials', Differentsial′nye Uravneniya i Primenen - Trudy Sem. Processov Optimal. Upravleniya. I Sekciya 1 (1971) 84-90.
7. A. G. Khovanskii, Fewnomials, Translations of Mathematical Monographs 88 (American Mathematical Society, Providence, RI, 1991).
8. T. Kiang, 'On the critical points of non-degenerate Newtonian potentials', Amer. J. Math. 54 (1932) 92-109.
9. V. V. Kozlov, 'A problem of Kelvin', J. Appl. Math. Mech. 81 (1990) 133-135.
10. A. G. Kušnirenko, 'Newton polyhedra and Bezout's theorem', Funktsional. Anal. i Priložen. 10 (1976) no.3, 82-83.
11. M. Marden, Geometry of polynomials (American Mathematical Society, Providence, RI, 1949).
12. J. C. Maxwell, A treatise on electricity and magnetism, vol.1, republication of the 3rd revised edition (Dover, New York, 1954).
13. P. McMullen and G. C. Shephard, Convex polytopes and the upper bound conjecture (Cambridge University Press, 1971).
14. M. Morse and S. Cairns, Critical point theory in global analysis and differential topology (Academic Press, New York, 1969).
15. T. S. Motzkin and J. L. Walsh, 'Equilibrium of inverse-distance forces in 3 dimensions', Pacific J. Math. 44 (1973) 241-250.
16. P. Orlik and H. Terao, 'The number of critical points of a product of powers of linear functions', Invent. Math. 120 (1995) 1-14.
17. F. Preparata and M. Shamos, Computational geometry: an introduction (Springer, Berlin, 1985).
18. R. Seidel, 'The complexity of Voronoi diagrams in higher dimensions', Proceedings of the Allerton Conference on Communication, Control, and Computing 20 (University of Illinois at Urbana- Champaign, 1982) 94-95.
19. D. Siersma, 'Voronoi diagrams and Morse theory of the distance function', Geometry in present day science (ed. O. E. Barndorff-Nielsen and E. B. V. Jensen; World Scientific, Singapore, 1999) 187-208.
20. A. Varchenko, 'Critical points of the product of powers of linear functions and families of bases of singular vectors', Compositio Math. 97 (1995) 385-401.