Smoothness of the Convex Hull of Planar Brownian Motion
Smoothness of the Convex Hull of Planar Brownian Motion
In this article we prove that for each $t > 0$, almost surely $\partial C(t)$, the boundary of the convex hull of two dimensional Brownian motion up to time $t$, is a $C^1$ curve in the plane. We also prove that if $\eta$ is a modulus of continuity such that …