Is there any real analytic diffeomorphism from two dimensional disk to itself, except to the identity, such that whose restriction to the boundary is identity?
Real analytic diffeomorphisms of the disk
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algebraic-topology
differential-topology
geometric-topology
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0If your diffeomorphism restricts to the interior of the disk into itself, then I think the Schwarz lemma applies, and it must be a rotation. – 2011-11-30
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0Yes Leonardo! In my case they send the interior into itself! Would you please write me a reference for the Schwarz lemma? and explain more? – 2011-11-30
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4@Leandro: the question specifies the map is only *real* analytic, so it need not be *complex* analytic. So Schwarz isn't relevant unless you can argue the map has to be complex analytic. – 2011-11-30
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2The common element in Jonas's response and my own is that in the real analytic category there are functions that behave much like bump functions, so you have a fair bit of freedom to manipulate functions, at least at the $C^0$ level. – 2011-11-30
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0@Ryan: you're right. My bad! – 2011-12-01