| 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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| 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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