Geometry of moduli spaces for low dimensional manifolds

2016 Fiscal Year Final Research Report

• Project/Area Number: 24340009
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Gakushuin University (2013-2016); Tohoku University (2012)
• Principal Investigator: Yamada Sumio 学習院大学, 理学部, 教授 (90396416)
• Co-Investigator(Kenkyū-buntansha): 大鹿 健一 大阪大学, 理学(系)研究科(研究院), 教授 (70183225) ; 山口 孝男 京都大学, 理学(系)研究科(研究院), 教授 (00182444)
• Research Collaborator: PAPADOPOULOS Athanase ストラスブルグ大学, 高等数学研究所, 研究ディレクター
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 微分幾何学 / 双曲計量 / アインシュタイン計量 / 一般相対性理論 / タイヒミュラー空間 / CAT(0)空間 / 調和写像

Outline of Final Research Achievements

Before the 19th century, the objects of mathematical interests tended to be individual phenomenon, whether it was a curve, a function, or a shape. In contrast, in the context of modern mathematics, the importance of analyzing a FAMILY of objects concurrently was recognized, and systematically pursued. In this research project, we focused on the topic of Einstein metrics in the general relativity, and that of hyperbolic metrics defined on two dimensional manifolds. Consequently we obtained a new and complete understanding of the moduli space consisting of all the static solutions to the Einstein-Maxwell equations, and a new connection between the global aspects of the Teichmueller theory and convex geometry and convex analysis.

Free Research Field

幾何解析