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- W4384200438 abstract "We consider the problem of finding an N-point configuration on the sphere $$S^dsubset mathbb R^{d+1}$$ with the smallest absolute maximum value over $$S^d$$ of its total potential. The potential induced by each point $$textbf{y}$$ in a given configuration at a point $$textbf{x}in S^d$$ is $$fleft( left| textbf{x}-textbf{y}right| ^2right) $$ , where f is continuous on [0, 4] and completely monotone on (0, 4], and $$left| textbf{x}-textbf{y}right| $$ is the Euclidean distance between points $$textbf{x}$$ and $$textbf{y}$$ . We show that any sharp point configuration $$overline{omega }_N$$ on $$S^d$$ , which is antipodal or is a spherical design of an even strength is a solution to this problem. We also prove that the absolute maximum over $$S^d$$ of the potential of any such configuration $$overline{omega }_N$$ is attained at points of $$overline{omega }_N$$ ." @default.
- W4384200438 created "2023-07-14" @default.
- W4384200438 creator A5052863100 @default.
- W4384200438 date "2023-07-13" @default.
- W4384200438 modified "2023-09-30" @default.
- W4384200438 title "Min-Max Polarization for Certain Classes of Sharp Configurations on the Sphere" @default.
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- W4384200438 doi "https://doi.org/10.1007/s00365-023-09661-1" @default.
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