  The isoperimetric inequalities for the expected lifetime of Brownian motion
state that the $L^p$-norms of the expected lifetime in a bounded domain for
$1\leq p\leq \infty$ are maximized when the region is a ball with the same
volume. In this paper, we prove quantitative improvements of the inequalities.
Since the isoperimetric properties hold for a wide class of L\'evy processes,
many questions arise from these improvements.
