We prove that, for any covering of a unit d-dimensional Euclidean ball by smaller balls, the sum of radii of the balls from the covering is greater than d. We also investigate the problem of finding lower and upper bounds for the sum of powers of radii of the balls covering a unit ball.
Glazerin, Alexey, "Covering a Ball by Smaller Balls" (2018). Mathematical and Statistical Sciences Faculty Publications and Presentations. 46.
Discrete & Computational Geometry