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