| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
The conjecture that the Gauss map of an algebraic minimal surface M in the Euclidean 3-space omits at most 2 points is a long standing problem. We lift the Gauss map to the universal covering of the surface, which is invariant under the action of the fundamental group of M, and apply the Nevanlinna theory to the lifted g.
1. We obtain the upper bound of κ which estimate the growth order of the characteristic function of g. 2. The ratio of the spherical area of the image of the Gauss map from the universal covering, and the hyperbolic area of the disk is bounded below by certain way. 3. Clarify the geometric meaning of the Lemma on logarithmic derivative. 4.We put the coordinate function as a power of the exponential function, then translate the no real period condition into that the absolute value of the exponential function is invariant. This is a use of the period condition in the most effective way to induce a defect relation.
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