Quantitative Inequalities for the Expected Lifetime of Brownian Motion
Daesung Kim · The Michigan Mathematical Journal · 2020
The isoperimetric inequalities for the expected lifetime of Brownian motion state that the Lp-norms of the expected lifetime in a bounded domain for 1≤p≤∞ 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 Lévy processes, many questions arise from these improvements.