Mykhailo Bilogliadov

activity

20142016

collaborators

4 papers

math.CA2016

Minimum Riesz Energy Problem on the Hyperdisk

Mykhailo Bilogliadov

We consider the minimum Riesz $s$ -energy problem on the unit disk $D := {(x_{1}, \dots, x_{d}) \in R^{d} : x_{1} = 0, x_{2}^{2} + x_{3}^{2} + \dots + x_{d}^{2} \leq 1}$ in the Euclidean space $\ma…

math.CA2016

Minimum Energy Problem on the Hypersphere

Mykhailo Bilogliadov

We consider the minimum energy problem on the unit sphere $S^{d - 1}$ in the Euclidean space $R^{d}$ , $d \geq 3$ , in the presence of an external field $Q$ , where the cha…

math.CA2015

Weighted energy problem on the unit sphere

Mykhailo Bilogliadov

We consider the minimal energy problem on the unit sphere $S^{2}$ in the Euclidean space $R^{3}$ immersed in an external field $Q$ , where the charges are assumed to int…

math.CA2014

Equilibria of the field generated by point charges

Mykhailo Bilogliadov

We consider a special case of Maxwell's problem on the number of equilibrium points of the Riesz potential $1/ r^{2 β}$ (where $r$ is the Euclidean distance and $β$ is the Riesz para…