Recently, using the desingularization technique, a new family of complete properly embedded self-shrinkers asymptotic to cones in three dimensional Euclidean space has been constructed by Kapouleas-Kleene-Moeller and independently by Nguyen.

In this talk, we present the uniqueness of self-shrinking ends asymptotic to any given cone in general Euclidean space. The feature of our uniqueness result is that we do not require the control on the boundaries of self-shrinking ends or the rate of convergence to cones at infinity. As applications, we show that, there do not exist complete properly embedded self-shrinkers other than hyperplanes having ends asymptotic to rotationally symmetric cones.