  We describe the solutions to the problem of identifying the continuum in the
complex plane that minimizes the logarithmic capacity among all the continuum
that contain a prefixed finite set of points. This description can be
implemented numerically and this can be used to improve the estimates on the
Bloch-Landau constant and other related problems as the maximal expected
lifetime of the Brownian motion on domains of inner radius one or the principal
eigenvalue for the Laplace operator on such domains.
