Abstract
It is a well known fact that the Newtonian potential of a uniform mass distribution in an ellipsoid is equal to a quadratic polynomial inside the ellipsoid. Conversely, if K is a bounded solid in R m and its Newtonian potential is equal to a quadratic polynomial inside it, then K is an ellipsoid. P. Dive proved this result for m=3 in 1931, and in 1986 E. DiBenedetto and A. Friedman showed it to be true for all m ≥ 2. We use certain topological methods to obtain a simpler proof of this result.
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