Stability for the Dirichlet problem under continuous Steiner symmetrization (Q1591347)

The authors present a nice construction that deforms an arbitrary open set into a ball. During the transformation the measure of the set stays invariant, the first Dirichlet-Laplace eigenvalue keeps decreasing, and the \(k\)-th eigenvalue is continuous from the left. The construction is based on a sequence of Steiner symmetrizations, and each Steiner symmetrization is done continuously according to F. Brock's original method [\textit{F. Brock}, Math. Nachr. 172, 25-48 (1995; Zbl 0886.49010)].