Global properties and the theory of convergences of diffusion processes of measure spaces

• Project/Area Number: 26400062
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido University (2016-2017); Tohoku University (2014-2015)
• Principal Investigator: Masamune Jun 北海道大学, 理学研究院, 教授 (50706538)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2016: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2014: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
• Keywords: 保存則 / 再帰性 / リュービル性 / ディリクレ形式 / 本質的自己共役性 / ラプラシアン / 調和関数 / トーション関数 / エバンス・ポテンシャル / 2パラメーターブラウン運動 / マルコフ過程 / シュレディンガー作用素 / 単体的複体 / 保存性 / グリーンの公式

Outline of Final Research Achievements

In this research project, we aim to develop the global analysis of diffusion processes on measure spaces associated with some Markov processes. The main results in this projects are (1) conservation property and recurrence of general Markov processes in terms of Green's formula (2) Characterizations of Liouville type problems of Riemannian manifolds and graphs (3) Generalized conservation property of Brownian motion with killing inside and its characterizations (4) Probabilisitic characterization of the essential selfadjointness of the Laplacian of Euclidean space removed a compact set.

Research Products

• [Int'l Joint Research] Bielefeld University/Jena University(Germany)
• [Int'l Joint Research] Bielefeld University(ドイツ)
• [Int'l Joint Research] CUNY(米国)
• [Int'l Joint Research] CUNY(米国)
• [Int'l Joint Research] Jena/Potsdam/Bielefeld(Germany)
• [Journal Article] Endothelial monolayer permeability under controlled oxygen tension (2017)
  • Author(s): Funamoto, K; Yoshino, D; Matsubara, K; Zervantonakis, I; Funamoto, K; Nakayama, M; Masamune, J; Kimura, J; Roger, K
  • Journal Title: Integrative Biology Volume: 6 Issue: 6 Pages: 529-538
  • DOI: 10.1039/c7ib00068e
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] robabilistic characterizations of essential self-adjointness and removability of singularities (2017)
  • Author(s): Hinz, M; Kang, S; Masamune, J
  • Journal Title: Science Journal of Volgograd State University. Mathematics. Volume: 3 Pages: 148-162
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Global properties of Dirichlet forms in terms of Green's formula (2017)
  • Author(s): Haeseler, S; Lenz, D; Keller, M; Masamune, J; Schmidt, S.
  • Journal Title: Calculus of Variations and PDEs Volume: 56 Issue: 5 Pages: 1-43
  • DOI: 10.1007/s00526-017-1216-7
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Presentation] A conservation property of Brownian motion with killing of a Riemannian manifold (2017)
  • Author(s): Masamune, J
  • Organizer: Analysis and PDEs on Manifolds
  • Int'l Joint Research / Invited
• [Presentation] Generalized conservation property (2017)
  • Author(s): Masamune, J
  • Organizer: Japanese-German Open Conference on Stochastic Analysis 2017
  • Int'l Joint Research / Invited
• [Presentation] H-convergence on Riemannian manifolds (2017)
  • Author(s): Masamune, J
  • Organizer: Analysis and Geometry on Graphs and Manifolds
  • Int'l Joint Research / Invited
• [Presentation] Existence of integrable harmonic functions on a complete Riemannian manifold (2017)
  • Author(s): Masamune, J
  • Organizer: Kyushu Probability Seminar
  • Invited
• [Presentation] Existence of integrable non-trivial harmonic functions on complete manifolds (2017)
  • Author(s): Masamune, J
  • Organizer: Mathematical Aspects of Quantum Fields and Related Topics
  • Invited
• [Presentation] On the Liouville property of harmonic functions (2016)
  • Author(s): Jun Masamune
  • Organizer: FS Diskrete Spektralgeometrie
  • Place of Presentation: Potsdam University Germany
  • Year and Date: 2016-03-12
  • Int'l Joint Research / Invited
• [Presentation] Stochastic completeness at infinity of a Riemannian manifold (2016)
  • Author(s): 正宗淳
  • Organizer: 月曜解析セミナー
  • Place of Presentation: 北海道大学（北海道・札幌市）
• [Presentation] Essential selfadjointness of the Laplacian and 2-parameter Brownian motion (2016)
  • Author(s): 正宗淳
  • Organizer: 量子系の数理と物質制御への展開II：量子ウォークを架け橋に
  • Place of Presentation: 東北大学（宮城県・仙台市）
  • Int'l Joint Research / Invited
• [Presentation] On the L1 Liouville property of a manifold with ends (2016)
  • Author(s): 正宗淳
  • Organizer: Geometry and Probability
  • Place of Presentation: RIMS（京都府・左京区）
  • Int'l Joint Research / Invited
• [Presentation] Constructions of non-trivial integrable harmonic functions on narrow or ample manifolds (2016)
  • Author(s): 正宗淳
  • Organizer: Math Colloquium
  • Place of Presentation: 北海道大学（北海道・札幌市）
• [Presentation] Variational convergence on Riemannian manifolds (2015)
  • Author(s): Jun Masamune
  • Organizer: Stochastic Analysis and Applications
  • Place of Presentation: Tohoku University Japan
  • Year and Date: 2015-08-31
  • Int'l Joint Research / Invited
• [Presentation] A "permeability" defined through singular perturbations (2015)
  • Author(s): Jun Masamune
  • Organizer: The mathematics of materials science: Ginzburg-Landau theory and related topics
  • Place of Presentation: CAMP South Korea
  • Year and Date: 2015-08-15
  • Int'l Joint Research / Invited
• [Presentation] ディリクレ形式の大域的性質 (2015)
  • Author(s): 正宗淳
  • Organizer: 応用解析研究会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2015-06-20
  • Invited
• [Presentation] Essential self-adjointness of the Hodge-Laplacian and p-negligible boundary (2015)
  • Author(s): Jun Masamune
  • Organizer: Workshop at Kansai University
  • Place of Presentation: 関西大学
  • Year and Date: 2015-01-31
  • Invited
• [Presentation] Distance and conservation property of jump processes (2014)
  • Author(s): Jun Masamune
  • Organizer: 談話会
  • Place of Presentation: 金沢大学
  • Year and Date: 2014-10-29
  • Invited
• [Presentation] On a long-term behavior of the jump process generated by a non-local operator (2014)
  • Author(s): Jun Masamune
  • Organizer: Geometry seminar
  • Place of Presentation: Nantes University, France
  • Year and Date: 2014-05-12
  • Invited
• [Remarks] Masamune Jun
  • URL: http://www.math.sci.hokudai.ac.jp/~jmasamune/
• [Funded Workshop] Dirichlet forms and their geometry (2017)
  • Place of Presentation: 東北大学（宮城県・仙台市）
  • Year and Date: 2017-03-18
• [Funded Workshop] Global properties in potential theory of continuous and discrete spaces (2017)
• [Funded Workshop] Interface between Commutative and Non-Commutative Stochastic Analysis (2017)
• [Funded Workshop] Dirichlet forms and their geometry (2017)
• [Funded Workshop] Workshop on Interface between Commutative and Non-Commutative Stochastic Analysis (2017)
  • Place of Presentation: 北海道大学（北海道・札幌市）