Scala-flat complete Kaehler metrics and K-stability at infinity
| Project/Area Number |
26610015
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Nagoya University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 代数的極小翼面 / 周期条件 / 自由フックス群 / 放物型局所化原理 / ネヴァンリンナ理論 / 対数微分補題 / ガウス写像 / 力学系 / 代数的極小曲面 / 放物型変換 / Osserman理論 / 量子化 / Nevanlinna理論 / 定スカラー曲率ケーラー計量 / K 安定性 / 完備スカラー平坦ケーラー計量 / 集団コーンフォッセン不等式 / 修正ケーラーリッチ流 / 離散化 / 修正リッチイテレーション / モンジュアンペール方程式 / 代数的極小曲面のガウス写像 / 放物型変換による集中現象 / 周期条件と対数微分の補題 |
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| Outline of Final Research Achievements |
By replacing an albebraic minimal surface by the triple consisting of the disc (the universal cover), the action of free Fuchsian group (fundamental group) and the period condition, we formulate a theory for all algebraic minimal surfaces. By applying the free Fuchsian group to a fixed fundamental domain, we get a dynamical system on the circle consisting of increasing number of vertices of fundamental domains whose evolution is governed by increasing word length. The properties of this dynamical system was formulated as the parabolic localization principle. I propose a pair of a meromorphic function exp(H) and a potentially infinite degree divisor D on the Riemann sphere, (exp(H),D), which encodes the period condition. The parabolic localization principle implies that the Gauss map is in the maximal approximation state relative to D. So is exp(H). It follows that the LLD (lemma on log derivative) applied to the pair (exp(H),D) decodes the period condition.
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Report
(5 results)
Research Products
(18 results)
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[Presentation] 満渕汎関数2015
Author(s)
小林亮一
Organizer
満渕俊樹教授退職記念シンポジウム
Place of Presentation
大阪大学
Year and Date
2015-03-12 – 2015-03-13
Related Report
Invited
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