Performance information

• Liouville theorem for V-harmonic maps under non-negative (m,V)-Ricci curvature for non-positive m　　　　　　　　　　　　　　　
  Kazuhiro Kuwae; Songzi Li; Xiang-Dong Li; Yohei Sakurai
  Stochastic Processes and their Applications, Volume：168, Feb. 2024, [Reviewed]
  Elsevier BV, Scientific journal
  DOI：https://doi.org/10.1016/j.spa.2023.104270
  DOI ID：10.1016/j.spa.2023.104270, ISSN：0304-4149
• Hamilton-type entropy formula along the Ricci flow on surfaces with boundary　　　　　　　　　　　　　　　
  Keita Kunikawa; Yohei Sakurai
  Communications in Analysis and Geometry, Volume：31, Number：7, First page：1655, Last page：1668, 2023, [Reviewed]
  International Press of Boston, Scientific journal
  DOI：https://doi.org/10.4310/cag.2023.v31.n7.a2
  DOI ID：10.4310/cag.2023.v31.n7.a2, ISSN：1019-8385, eISSN：1944-9992
• Maximal diameter theorem for directed graphs of positive Ricci curvature　　　　　　　　　　　　　　　
  Ryunosuke Ozawa; Yohei Sakurai; Taiki Yamada
  Communications in Analysis and Geometry, Volume：31, Number：5, First page：1275, Last page：1298, 2023, [Reviewed]
  International Press of Boston, Scientific journal
  DOI：https://doi.org/10.4310/cag.2023.v31.n5.a7
  DOI ID：10.4310/cag.2023.v31.n5.a7, ISSN：1019-8385, eISSN：1944-9992
• Comparison geometry of manifolds with boundary under lower $N$-weighted Ricci curvature bounds with $\varepsilon$-range　　　　　　　　　　　　　　　
  Kazuhiro KUWAE; Yohei SAKURAI
  Journal of the Mathematical Society of Japan, Volume：75, Number：1, First page：151, Last page：172, Jan. 2023, [Reviewed]
  Mathematical Society of Japan (Project Euclid), Scientific journal
  DOI：https://doi.org/10.2969/jmsj/87278727
  DOI ID：10.2969/jmsj/87278727, ISSN：0025-5645
• Dirichlet problem for harmonic maps from strongly rectifiable spaces into regular balls in $${\text {CAT } }(1)$$ spaces
  Yohei Sakurai
  Annals of Global Analysis and Geometry, Volume：64, Number：3, 2023, [Reviewed]
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s10455-023-09924-x
  DOI ID：10.1007/s10455-023-09924-x, ISSN：0232-704X, eISSN：1572-9060
• Heat Flow and Concentration of Measure on Directed Graphs with a Lower Ricci Curvature Bound
  Ryunosuke Ozawa; Yohei Sakurai; Taiki Yamada
  Potential Analysis, Volume：59, Number：3, First page：955, Last page：969, Mar. 2022, [Reviewed]
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s11118-022-09994-9
  DOI ID：10.1007/s11118-022-09994-9, ISSN：0926-2601, eISSN：1572-929X
• Yau and Souplet-Zhang type gradient estimates on Riemannian manifolds with boundary under Dirichlet boundary condition
  Keita Kunikawa; Yohei Sakurai
  Proceedings of the American Mathematical Society, Volume：150, Number：4, First page：1767, Last page：1777, Jan. 2022, [Reviewed]
  

  In this paper, on Riemannian manifolds with boundary, we establish a Yau type gradient estimate and Liouville theorem for harmonic functions under Dirichlet boundary condition. Under a similar setting, we also formulate a Souplet-Zhang type gradient estimate and Liouville theorem for ancient solutions to the heat equation.

  
  American Mathematical Society (AMS), Scientific journal
  DOI：https://doi.org/10.1090/proc/15768
  DOI ID：10.1090/proc/15768, ISSN：0002-9939, eISSN：1088-6826
• Rigidity phenomena on lower N-weighted Ricci curvature bounds with ε-range for nonsymmetric Laplacian
  Kazuhiro Kuwae; Yohei Sakurai
  Illinois Journal of Mathematics, Volume：65, Number：4, First page：847, Last page：868, Dec. 2021, [Reviewed]
  Duke University Press, Scientific journal
  DOI：https://doi.org/10.1215/00192082-9619586
  DOI ID：10.1215/00192082-9619586, ISSN：0019-2082
• One dimensional weighted Ricci curvature and displacement convexity of entropies
  Yohei Sakurai
  Mathematische Nachrichten, Volume：294, Number：10, First page：1950, Last page：1967, Sep. 2021, [Reviewed]
  Abstract
  
  In the present paper, we prove that a lower bound on the 1‐weighted Ricci curvature is equivalent to a convexity of entropies on the Wasserstein space. Based on such characterization, we provide some interpolation inequalities such as the Prékopa–Leindler inequality, the Borel–Branscamp–Lieb inequality, and the Brunn–Minkowski inequality under the curvature bound.
  Wiley, Scientific journal
  DOI：https://doi.org/10.1002/mana.201900143
  DOI ID：10.1002/mana.201900143, ISSN：0025-584X, eISSN：1522-2616
• Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry
  Keita Kunikawa; Yohei Sakurai
  Calculus of Variations and Partial Differential Equations, Volume：60, Number：5, Aug. 2021, [Reviewed]
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s00526-021-02079-2
  DOI ID：10.1007/s00526-021-02079-2, ISSN：0944-2669, eISSN：1432-0835
• Liouville Theorem for Heat Equation Along Ancient Super Ricci Flow Via Reduced Geometry
  Keita Kunikawa; Yohei Sakurai
  The Journal of Geometric Analysis, Volume：31, Number：12, First page：11899, Last page：11930, Jun. 2021, [Reviewed]
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s12220-021-00705-1
  DOI ID：10.1007/s12220-021-00705-1, ISSN：1050-6926, eISSN：1559-002X
• Geometric and spectral properties of directed graphs under a lower Ricci curvature bound
  Ryunosuke Ozawa; Yohei Sakurai; Taiki Yamada
  Calculus of Variations and Partial Differential Equations, Volume：59, Number：4, Aug. 2020, [Reviewed]
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s00526-020-01809-2
  DOI ID：10.1007/s00526-020-01809-2, ISSN：0944-2669, eISSN：1432-0835
• Upper bounds for higher-order Poincaré constants
  Kei Funano; Yohei Sakurai
  Transactions of the American Mathematical Society, Volume：373, Number：6, First page：4415, Last page：4436, Mar. 2020, [Reviewed]
  

  Here we introduce higher-order Poincaré constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of the weighted Laplacian and the first nontrivial eigenvalue of the -Laplacian. In the case of the closed eigenvalue problem and the Neumann eigenvalue problem these are related to the estimates obtained by Chung-Grigor’yan-Yau and Gozlan-Herry. We also obtain similar upper bounds for Dirichlet eigenvalues and multi-way isoperimetric constants. As an application, for manifolds with boundary of nonnegative dimensional weighted Ricci curvature, we give upper bounds for inscribed radii in terms of dimension and the first Dirichlet Poincaré constant.

  
  American Mathematical Society (AMS), Scientific journal
  DOI：https://doi.org/10.1090/tran/8049
  DOI ID：10.1090/tran/8049, ISSN：0002-9947, eISSN：1088-6850
• Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold
  Kei Funano; Yohei Sakurai
  Proceedings of the American Mathematical Society, Volume：147, Number：7, First page：3155, Last page：3164, Mar. 2019, [Reviewed]
  American Mathematical Society (AMS), Scientific journal
  DOI：https://doi.org/10.1090/proc/14430
  DOI ID：10.1090/proc/14430, ISSN：0002-9939, eISSN：1088-6826
• Rigidity of manifolds with boundary under a lower Bakry-Émery Ricci curvature bound　　　　　　　　　　　　　　　
  Yohei Sakurai
  Tohoku Mathematical Journal, Volume：71, Number：1, First page：69, Last page：109, Mar. 2019, [Reviewed]
  Mathematical Institute, Tohoku University, Scientific journal
  DOI：https://doi.org/10.2748/tmj/1552100443
  DOI ID：10.2748/tmj/1552100443, ISSN：0040-8735
• Comparison Geometry of Manifolds with Boundary under a Lower Weighted Ricci Curvature Bound
  Yohei Sakurai
  Canadian Journal of Mathematics, Volume：72, Number：1, First page：243, Last page：280, Oct. 2018, [Reviewed]
  Abstract
  
  We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition and a suitable condition for the weighted mean curvature for the boundary, we obtain various comparison geometric results.
  Canadian Mathematical Society, Scientific journal
  DOI：https://doi.org/10.4153/s0008414x1800007x
  DOI ID：10.4153/s0008414x1800007x, ISSN：0008-414X, eISSN：1496-4279
• Rigidity Phenomena in Manifolds with Boundary Under a Lower Weighted Ricci Curvature Bound
  Yohei Sakurai
  The Journal of Geometric Analysis, Volume：29, Number：1, First page：1, Last page：32, Oct. 2018, [Reviewed]
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s12220-017-9871-7
  DOI ID：10.1007/s12220-017-9871-7, ISSN：1050-6926, eISSN：1559-002X
• Rigidity of manifolds with boundary under a lower Ricci curvature bound　　　　　　　　　　　　　　　
  Yohei Sakura
  Osaka Journal of Mathematics, Volume：54, Number：1, First page：85, Last page：119, 2017, [Reviewed]

• 様々な空間上の比較幾何学　　　　　　　　　　　　　　　
  Apr. 2023 - Mar. 2028
  Grant amount(Total)：4550000, Direct funding：3500000, Indirect funding：1050000
  Grant number：23K12967
• Analysis on metric measure spaces by optimal transport theory and Markov processes　　　　　　　　　　　　　　　
  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (S), Apr. 2022 - Mar. 2027
  Fukuoka University
  Grant amount(Total)：97760000, Direct funding：75200000, Indirect funding：22560000
  Grant number：22H04942
• Ricci曲率の概念を持つ離散空間上の幾何解析　　　　　　　　　　　　　　　
  Aug. 2021 - Mar. 2023
  Grant amount(Total)：3120000, Direct funding：2400000, Indirect funding：720000
  Grant number：21K20315