| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
We intend to generalize Nevanlinna theory which is a main method in the study of value distribution theory of holomorphic maps by using probabilistic methods. We obtained a second main theorem of Nevanlinna theory for meromorphic functions on general domains in complex Euclidean spaces. In the generalization process, we introduce a notion of default functions into the study of function theory. As its applications we obtained new Liouville type theorems for subharmonic functions and harmonic maps. We also extended our generalization ideas to consider an analogy of Riemann-Roch theorem on infinite, locally finite, connected graphs.
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