Quasiharmonic removability of the separating set in Example 2.16(c)

Determine whether the unbounded closed set \(F_3\) in Example 2.16(c) is removable for bounded quasiharmonic functions in \(G_3=(-2,-1)\cup(1,2)\).

Background

In part (c), the authors construct bounded $p$-harmonic extensions across the unbounded closed set $F_3$, even though the domain $G_3$ is disconnected. Thus removability is established for bounded $p$-harmonic functions.

Whether the same removability holds for bounded quasiharmonic functions, which allow a quasiminimizing constant $Q>1$, remains unresolved. This example further illustrates the limits of extending the compact-set theory to unbounded closed sets.