an:00768210
Zbl 0830.31003
Karp, Lavi
On the Newtonian potential of ellipsoids
EN
Complex Variables, Theory Appl. 25, No. 4, 367-371 (1994).
00026791
1994
j
31B20
Newtonian potential of a uniform mass distribution; topological methods
It is known that the Newtonian potential of a uniform mass distribution of an ellipsoid is equal to a quadratic polynomial inside the ellipsoid. In 1931 \textit{P. Dive} [Bull. Soc. Math. Fr. 59, 128-140 (1931; Zbl 0004.16601)]\ proved that the converse is valid -- if \(K\) is a bounded solid in \(\mathbb{R}^3\) and its Newtonian potential is equal to a quadratic polynomial inside it, then \(K\) is an ellipsoid; in 1986 \textit{E. DiBenedetto} and \textit{A. Friedman} [Indiana Univ. Math. J. 35, 573-606 (1986; Zbl 0667.35074)]\ generalized this result to the case of \(\mathbb{R}^m\), \(m > 2\).
The author uses some topological methods to obtain a simpler proof of that result.
M.Dont (Praha)
Zbl 0667.35074; Zbl 0004.16601