Shin-ichi OHTA

Department of Mathematics, Osaka University;

RIKEN Center for Advanced Intelligence Project (AIP)

Mathematical Science Team
Mathematical Analysis Team (closed March 2022)

Workshops: Geometry and Probability (2007-), SHIOYA 60 (2023)

Research interest

Comparison geometry involving various kinds of curvature, and its applications.
Keywords:
Riemannian geometry, Alexandrov spaces, CAT-spaces, analysis on metric measure spaces,
optimal transport theory, Wasserstein geometry, gradient flows, optimization,
Finsler geometry, Lorentz-Finsler geometry (Finsler spacetimes), the geometry of Banach spaces, ...
Here is my brief curriculum vitae.

Book

  1. Comparison Finsler Geometry, Springer Monographs in Mathematics, Springer, Cham, 2021.
    https://link.springer.com/book/10.1007/978-3-030-80650-7

Preprints

  1. (with Erasmo CAPONIO & Argam OHANYAN)
    Splitting theorems for weighted Finsler spacetimes via the p-d'Alembertian: beyond the Berwald case, Dec 2024 (PDF).
  2. (with Victor-Emmanuel BRUNEL & Jordan SERRES)
    A generalization of Grünbaum's inequality in RCD(0,N)-spaces, Aug 2024 (PDF).
  3. (with Kohei SUZUKI)
    Integral Varadhan formula for non-linear heat flow, Mar 2024 (PDF).
  4. How does the contraction property fail for convex functions on normed spaces?, Nov 2023 (Revised 27 May 2024 PDF).
  5. (with Wei ZHAO)
    Gradient flows in asymmetric metric spaces and applications, Jun 2022 (Revised 20 Jul 2023 PDF),
    to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci.
  6. Discrete-time gradient flows in Gromov hyperbolic spaces, May 2022 (Revised 31 Jan 2025 PDF),
    to appear in Israel J. Math.
  7. (with Kei KONDO & Minoru TANAKA)
    A Toponogov type triangle comparison theorem in Finsler geometry, May 2012 (PDF).

Recently published papers

(PDF files are of preprint versions, they may be different from published ones.)
  1. Barycenters and a law of large numbers in Gromov hyperbolic spaces, Rev. Mat. Iberoam. 40 (2024), 1185-1206 (PDF).
  2. (with Mathias BRAUN)
    Optimal transport and timelike lower Ricci curvature bounds on Finsler spacetimes, Trans. Amer. Math. Soc. 377 (2024), 3529-3576 (PDF).
  3. (with Yufeng LU & Ettore MINGUZZI)
    Geometry of weighted Lorentz-Finsler manifolds II: A splitting theorem, Internat. J. Math. 34 (2023), no. 1, 2350002 (PDF).
  4. (with Cong Hung MAI)
    Quantitative estimates for the Bakry-Ledoux isoperimetric inequality. II, Bull. Lond. Math. Soc. 55 (2023), 224-233 (PDF).
  5. A semigroup approach to Finsler geometry: Bakry-Ledoux's isoperimetric inequality, Comm. Anal. Geom. 30 (2022), 2347-2387 (PDF).
  6. (with Yufeng LU & Ettore MINGUZZI)
    Comparison theorems on weighted Finsler manifolds and spacetimes with ε-range, Anal. Geom. Metr. Spaces 10 (2022), 1-30 (PDF).
  7. (with Cong Hung MAI)
    Quantitative estimates for the Bakry-Ledoux isoperimetric inequality, Comment. Math. Helv. 96 (2021), 693-739 (PDF).
  8. (with Yufeng LU & Ettore MINGUZZI)
    Geometry of weighted Lorentz-Finsler manifolds I: Singularity theorems, J. Lond. Math. Soc. (2) 104 (2021), 362-393 (PDF).

All publications

Some corrections

  1. Needle decompositions and isoperimetric inequalities in Finsler geometry, J. Math. Soc. Japan 70 (2018), 651-693 (PDF).
    (K,N)-convexity and the curvature-dimension condition for negative N, J. Geom. Anal. 26 (2016), 2067-2096 (PDF).
    Finsler interpolation inequalities, Calc. Var. Partial Differential Equations 36 (2009), 211-249 (PDF).
    *Correction (PDF).
  2. Some functional inequalities on non-reversible Finsler manifolds, Proc. Indian Acad. Sci. Math. Sci. 127 (2017), 833-855 (PDF).
    *Correction: 131 (2021), Paper No. 23, 2pp. (PDF).
  3. Nonlinear geometric analysis on Finsler manifolds, Eur. J. Math. 3 (2017), 916-952 (PDF).
    *Correction (PDF).
  4. Vanishing S-curvature of Randers spaces, Differential Geom. Appl. 29 (2011), 174-178 (PDF).
    *Correction (PDF).

Articles in Japanese