Points on Spheres and Manifolds

Computational Analysis on the Sphere and Other Manifolds Website

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Research Articles on the Sphere and other Manifolds

(217) Asymptotics of Weighted Best-Packing on Rectifiable Sets (with S. V. Borodachov and D. P. Hardin), accepted for publication in Math. Sbornik.
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(216) The Support of the Limit Distribution of Optimal Riesz Energy Points on Sets of Revolution in R³ (with J. Brauchart and D. Hardin), J. Math. Phys, 48 (2007), no. 12, 122901, 24 pp..
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(215) Menke Points on the Real Line and Their Connection to Classical Orthogonal Polynomials (with P. Mathur and J.S. Brauchart), submitted. Download: [PDF]

(212) Asymptotics of Best-Packing on Rectifiable Sets (with S.V. Borodachov and D.P. Hardin), Proc. Amer. Math. Soc., Vol. 135 (2007), pp. 2369-2380.
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(211) Riesz Spherical Potentials with External Fields and Minimal Energy Points Separation (with P. Dragnev), Potential Anal., Vol. 26, No. 2 (2007), pp. 139-162.
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(210) The Support of the Logarithmic Equilibrium Measure on Sets of Revolution in R³ (with D. Hardin and H. Stahl), J. Math. Phys., Vol. 48, No. 2 (2007), 022901, 14 pp.
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(208) Asymptotics for Discrete Weighted Minimal Riesz Energy Problems on Rectifiable Sets (with S.V. Borodachov and D.P. Hardin), Trans. Amer. Math. Soc., Vol. 360 (2008), pp. 1559-1580.
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(205) On Separation of Minimal Riesz Energy Points on Spheres in Euclidean Spaces (with A. B. J. Kuijlaars and X. Sun), Journal Comp. & Applied Math., Vol 199, No. 1 (2007), pp. 172-180.
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(201) Discretizing Manifolds via Minimum Energy Points
(with Doug Hardin), Notices of the American Mathematical Society, Vol. 51, No. 10 (2004), pp. 1186-1194.
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(199) Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds
(with Doug Hardin), Advances in Mathematics, Vol. 193, No. 1 (2005), pp. 174-204.
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(196) Asymptotics for Minimal Discrete Riesz Energy on Curves in R^d
(with A. Martínez-Finkelshtein, V. Maymeskul, and E.A. Rakhmanov), Canadian Journal of Mathematics, Vol. 56 (2004), pp. 529-552.
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(192) Note on d-extremal configurations for the Sphere in R^(d+1)
(with M. Goetz), Recent progress in multivariate approximation, Internat. Ser. Numer. Math., Birkhauser, Basel, Vol. 137 (2001), pp. 159-162.
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(161) Distributing Many Points on a Sphere
(with A.B.J. Kuijlaars), The Mathematical Intelligencer, Vol. 19, No. 1 (1997), pp. 5-11.
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(159) Asymptotics for Minimal Discrete Energy on the Sphere
(with A.B.J. Kuijlaars), Transactions of the American Mathematical Society, Vol. 350, No. 2 (1998), pp. 523-538.
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(156) Electrons on the Sphere
(with E.A. Rakhmanov and Y.M. Zhou), Computational Methods and Function Theory, (R. M. Ali, S. Ruscheweyh, and E. B. Saff, eds.), World Scientific, (1995), pp. 111-127.
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(155) Minimal Discrete Energy on the Sphere
(with E.A. Rakhmanov and Y.M. Zhou), Mathematical Research Letters, Vol. 1 (1994), pp. 647-662.
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A suggested improvement in the spiral points algorithm of Rakhmanov, Saff, and Zhou was found by
Knud Thomsen. See <http://groups.google.com/group/sci.math/browse_thread/thread/983105fb1ced42c/e803d9e3e9ba3d23#e803d9e3e9ba3d23>