An exact Lagrangian in a cotangent bundle that coincides witha cotangent fiber outside a compact set, and is disjoint from at leastone cotangent fiber is called a nearby Lagrangian fiber. I will explainjoint work in preparation with Yash Deshmukh and Alex Pieloch, showingthat any nearby Lagrangian fiber in T∗ℂℙ2or T∗(Sn−k×ℝk)issmoothly isotopic to a cotangent fiber rel boundary in the complement ofthe missed fiber. These results follows from a more general homotopyrigidity result for exact Lagrangian fillings of unknots in subcriticalWeinstein manifolds.