  Defect extremal surface is defined by minimizing the Ryu-Takayanagi surface
corrected by the defect theory, which is useful when the RT surface crosses or
terminates on the defect. Based on the decomposition procedure of a AdS bulk
with a defect brane, proposed in arXiv:2012.07612, we derive Page curve in a
time dependent set up of AdS$_3$/BCFT$_2$, and find that the result from island
formula agrees with defect extremal surface formula precisely. We then extend
the study to higher dimensions and find that the entropy computed from bulk
defect extremal surface is generally less than that from island formula in
boundary low energy effective theory, which implies that the UV completion of
island formula gives a smaller entropy in higher dimensions.
