| Co-Investigator(Kenkyū-buntansha) |
中西 敏浩 島根大学, 学術研究院理工学系, 教授 (00172354)
須川 敏幸 東北大学, 情報科学研究科, 教授 (30235858)
佐官 謙一 大阪市立大学, 大学院理学研究科, 特任教授 (70110856)
小森 洋平 早稲田大学, 教育・総合科学学術院, 教授 (70264794)
谷口 雅彦 奈良女子大学, 自然科学系, 教授 (50108974)
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| Budget Amount *help |
¥16,640,000 (Direct Cost: ¥12,800,000、Indirect Cost: ¥3,840,000)
Fiscal Year 2017: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2016: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2015: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
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| Outline of Final Research Achievements |
We introduced the Teichmueller space of diffeomorphisms of the unit circle with Hoelder continuous derivatives as a subspace of the universal Teichmueller space. We provided a complex Banach manifold structure for it and proved that its topology coincides with the one induced by the Hoelder constants of the maps. We also proved that the barycentric extension induces a continuous section from the Teichmueller space of the circle diffeomorphisms with respect to this topology. Then, we considered deformations of a group of circle diffeomorphisms with Hoelder continuous derivative and showed certain rigidity under conjugation by symmetric homeomorphisms of the circle. As an application, we give a condition for such a diffeomorphism group to be conjugate to a Moebius group by a diffeomorphism of the same regularity. The strategy is to find a fixed point of the group which acts isometrically on the integrable Teichmueller space with the Weil-Petersson metric.
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