2013 Fiscal Year Final Research Report
Probabilistic approach to analysis and geometry on metric measure spaces
| Project/Area Number |
22340036
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kumamoto University |
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Principal Investigator |
KUWAE Kazuhiro 熊本大学, 自然科学研究科, 教授 (80243814)
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| Co-Investigator(Kenkyū-buntansha) |
SHIOYA Takashi 東北大学, 理学研究科, 教授 (90235507)
OHTA Shinichi 京都大学, 理学研究科, 准教授 (00372558)
KUWADA Kazumasa 東京工業大学, 理学部, 准教授 (30432032)
ISHIWATA Satoshi 山形大学, 理学部, 准教授 (70375393)
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| Co-Investigator(Renkei-kenkyūsha) |
ATSUJI Atsushi 慶応大学, 経済学部, 教授 (00221044)
KAWABI Hiroshi 岡山大学, 自然科学研究科, 准教授 (80432904)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | ディリクレ形式 / 調和写像 / 劣調和関数 / 変分収束 / グロモフ・ハウスドルフ収束 / アレキサンドロフ空間 / 加藤クラス / 熱核 |
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| Research Abstract |
We obtained a Jensen's inequality over complete p-uniformly convex spaces. Further we proved the unique existence of the (non-linear) resolvent associated to a coercive proper lower semi continuous function satisfying a weaker notion of p-uniform convexity on a complete metric space and establish the existence of the minimizer of such functions as the large time limit of the non-linear resolvents, which generalizes the pioneering work by J. Jost for harmonic maps into CAT(0)-spaces. The results can be also applied to Lp-Wasserstein space over complete separable p-uniformly convex spaces. As an application, we solve an initial boundary value problem for p-harmonic maps into CAT(0)-spaces in terms of Cheeger type p-Sobolev spaces. On the other hand, we investigated the spectral bounds for symmetric Markov chains with positive n-step coarse Ricci curvature for not only functions but also maps into complete separable 2-uniformly convex spaces with geometric conditions.
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