Defect extremal surface for reflected entropy

Defect extremal surface is defined by extremizing the Ryu-Takayanagi formula corrected quantum defect theory. This interesting when AdS bulk contains a brane (or string). We introduce for reflected entropy, which mixed state generalization of entanglement entropy measure. Based on decomposition procedure an with brane, we demonstrate equivalence between and island in AdS$_3$/BCFT$_2$. also compute evolution evaporating black hole model find that agrees formula.