A four-dimensional Neumann ovaloid

Lavi Karp ORT Braude College Erik Lundberg Florida Atlantic University

Analysis of PDEs Geometric Analysis and Geometric Topology Numerical Analysis and Scientific Computing mathscidoc:1803.43015

Arkiv for Matematik, 55, 2017
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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  title={A four-dimensional Neumann ovaloid},
  author={Lavi Karp, and Erik Lundberg},
  booktitle={Arkiv for Matematik},
Lavi Karp, and Erik Lundberg. A four-dimensional Neumann ovaloid. 2017. Vol. 55. In Arkiv for Matematik. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180301170914906639950.
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