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arXiv · 1609.07702

A four--dimensional Neumann ovaloid

Lavi Karp·Erik Lundberg
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Abstract

What is the shape of a uniformly massive object that generates a gravitational potential equivalent to that of two equal point-masses? If the weight of each point-mass is sufficiently small compared to the distance between the points then the answer is a pair of balls of equal radius, one centered at each of the two points, but otherwise it is a certain domain of revolution about the axis passing through the two points. The existence and uniqueness of such a domain is known, but an explicit parameterization is known only in the plane where the region is referred to as a Neumann oval. We construct a four-dimensional "Neumann ovaloid", solving explicitly this inverse potential problem.

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Lavi Karp, Erik Lundberg. 2016-09-25. A four--dimensional Neumann ovaloid. https://arxiv.org/abs/1609.07702

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