(untitled) (Communications in Mathematical Research, 2021)
Let H_n be an orientable handlebody of genus n. It has been proved that for n not less than 2, there exists an annulus-busting curve in ∂H_n. In the present paper, we prove that for n not less than 2, there exists an essential simple closed curve C in ∂H_n which intersects each essential planar surface in H_n non-emptily. Furthermore, we show that for n not less than 3, a pants-busting curve must also be an annulus-busting curve.