Holomorphic curves and complex Monge-Ampere equation

• Project/Area Number: 15H06129
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: The University of Tokyo
• Principal Investigator: Tiba Yusaku 東京大学, 大学院数理科学研究科, 特任助教 (90635616)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 複素モンジュ・アンペール方程式 / 正則曲線 / モンジュ・アンペール方程式 / 正則写像 / ケーラー多様体 / モンジュ・アンペールカレント

Outline of Final Research Achievements

We study the relation between the complex Monge-Ampere equation and holomoprhic curves. As a result, we show a sufficient condition such that the complement of a entire maps in a compact Kahler manifold is pluri-polar set. This is a new property of entire maps. We use pluripotential theory to study holomorphic maps.

Research Products

• [Journal Article] The intersection of an entire holomorphic mapping and a complex Monge-Ampere current with a bounded potential (2016)
  • Author(s): Yusaku Tiba
  • Journal Title: Proceedings of the American Mathematical Society Volume: 144 Issue: 12 Pages: 5265-5273
  • DOI: 10.1090/proc/13295
  • Peer Reviewed
• [Presentation] The intersection of an entire holomorphic mapping and a complex Monge-Ampere current with a bounded potential (2016)
  • Author(s): 千葉優作
  • Organizer: 多変数関数論冬セミナー
  • Place of Presentation: 福岡工業大学
  • Year and Date: 2016-12-17
• [Presentation] Entire mappings and Monge-Amp\`ere currents with bounded potentials (2016)
  • Author(s): 千葉優作
  • Organizer: 複素解析幾何学のポテンシャル論的諸相
  • Place of Presentation: 東京大学数理科学研究科
  • Year and Date: 2016-02-12