Suppose $D_1$ and $D_2$ are two n-dimensional closed disks (topologically embedded) in the sphere $S^n$ ($n>=1$). Is there a homeomorphism $f:S^n \rightarrow S^n$ such that $f(D_1)=D_2$? Maybe I should ask whether all the embeddings of $D^n$ in $S^n$ are ambient isotopic?
When $n=1$, a disk is just a closed connected arc on the circle. There is an obvious construction using stretching and rotation. When $n=2$, Schoenflies theorem implies the result trivially. I am also interested in the smooth category.