Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting

We compute exactly the mean perimeter and area of convex hull a $2$-d Brownian motion duration $t$ diffusion constant $D$, in presence resetting to origin at rate $r$. show that for any $t$, is given by $\langle L(t)\rangle= 2 \pi \sqrt{\frac{D}{r}}\, f_1(rt)$ A(t) \rangle= 2\pi\frac{D}{r}\, f_2(rt)$ where scaling functions $f_1(z)$ $f_2(z)$ are computed explicitly. For large $t\gg 1/r$, grows extremely slowly as L(t)\rangle \propto \ln (rt)$ with time. Likewise, also A(t)\rangle \ln^2(rt)$ 1/r$. Our exact results indicate hull, resetting, approaches circular shape late times. Numerical simulations perfect agreement our analytical predictions.