| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
(1) We introduced the Teichmueller space of circle diffeomorphisms with Hoelder continuous derivatives and established its foundation. (2) We proved that if a group of Moebius transformations is conjugate to a group of circle diffeomorphisms with Hoelder continuous derivatives by a symmetric homeomorphism, then the conjugating map actually has a Hoelder continuous derivative of the same order. (3) We obtained a necessary and sufficient condition for a group of circle diffeomorphisms with α-Hoelder continuous derivatives for α>1/2 to be conjugate to a group of Moebius transformations by a circle diffeomorphism with an α-Hoelder continuous derivative in terms of uniform integrability of the complex dilatations of quasiconformal extensions of the group elements. (4) Even if we do not assume α>1/2, we showed that if the integrability of quasiconformal extensions is uniformly bounded by a certain constant sufficiently small, then the above result still holds true.
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