a variational problem with respect to conformal maps and a variational problem for pullbacks of metrics

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540213
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Yamaguchi University
• Principal Investigator: NAKAUCHI Nobumitsu 山口大学, 理工学研究科, 教授 (50180237)
• Co-Investigator(Kenkyū-buntansha): NAITOH Hiroo 山口大学, 大学院理工学研究科, 教授 (10127772)
• Co-Investigator(Renkei-kenkyūsha): KAWAI Shigeo 佐賀大学, 文化教育学部, 教授 (30186043) ; TAKAKUWA Shoichiro 首都大学東京, 大学院理工学研究科, 教授 (10183435)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 変分問題 / 共形写像 / 等角写像 / pullback / symphonic map / C-stationary map

Outline of Final Research Achievements

We give original researches on the following two maps: (1) stationary maps (we call them C-stationary maps) of the integral of the norm of a tensor which is a scale of the conformality of smooth maps between Riemannian manifolds, (2) stationary maps (we call them symphonic maps) of the integral of the norm of the pullback of metrics by smooth maps between Riemannian manifolds. We obtain results of regularity, a construction (we call it a symphonic join) and stability for symphonic maps. For C-stationary maps, we have partial results of stability, though it is considerably difficult to handle C-stationary maps.

Free Research Field

多様体上の変分問題