?. , Taking ? ?1 instead of ? if necessary, we can further suppose that, for any point x of

, Suppose for a contradiction that there exist a real number ? ? (0, ? 0 ) and a diffeomorphism g ? G 1 with the following properties. 1. The diffeomorphism g is increasing on

?. K. , There exists a point x 0 in

, ? ? and the diffeomorphism h is increasing on

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