On an Electrostatic Problem and a New Class of Exceptional Subdomains of \(\mathbb{R}^3\)
On an Electrostatic Problem and a New Class of Exceptional Subdomains of \(\mathbb{R}^3\)
We study the existence of nontrivial unbounded surfaces with the property that the constant charge distribution on is an electrostatic equilibrium, i.e., the resulting electrostatic force is normal to the surface at each point on . Among bounded regular surfaces , only the round sphere has this property by a …