Diffeomorphisms of circle extends to diffeomorphisms of disk

269 Views Asked by At

Any diffeomorphism of a circle can be extended to a diffeomorphism of a circle. I was trying to do it by using the Radó–Kneser–Choquet theorem as provided here. I did the proof which is given in the Duren's book Harmonic mappings in the plane. But, he only proves about the homeomorphism. How to prove the diffeomorphism. Any help!