Jana Björn

Liouville theorems and removable sets for bounded $p$-harmonic and quasiharmonic functions on metric spaces under local assumptions

For connected proper metric spaces $X$, equipped with a locally doubling measure supporting a local $p$-Poincar\'e inequality, we completely characterize which compact sets $K$ with positive capacity are removable for bounded $p$-harmonic functions, $p>1$. Similar results are proved also for bounded quasiharmonic funct...