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, 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 Victor-Emmanuel BRUNEL & Jordan SERRES)
    A generalization of Grünbaum's inequality in RCD(0,N)-spaces, Aug 2024 (PDF).
  2. (with Kohei SUZUKI)
    Integral Varadhan formula for non-linear heat flow, Mar 2024 (PDF).
  3. How does the contraction property fail for convex functions on normed spaces?, Nov 2023 (Revised 27 May 2024 PDF).
  4. (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.
  5. Discrete-time gradient flows in Gromov hyperbolic spaces, May 2022 (Revised 22 Jun 2023 PDF),
    to appear in Israel J. Math.
  6. (with Kei KONDO & Minoru TANAKA)
    A Toponogov type triangle comparison theorem in Finsler geometry, May 2012 (PDF).

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).
  9. (with Nina LEBEDEVA & Vladimir ZOLOTOV)
    Self-contracted curves in spaces with weak lower curvature bound, Int. Math. Res. Not. IMRN. 2021 (2021), 8623-8656 (PDF).
  10. (with Nicola GIGLI, Christian KETTERER & Kazumasa KUWADA)
    Rigidity for the spectral gap on RCD(K,∞)-spaces, Amer. J. Math. 142 (2020), 1559-1594 (PDF).
  11. (with Asuka TAKATSU)
    Equality in the logarithmic Sobolev inequality, Manuscripta Math. 162 (2020), 271-282 (PDF).
  12. Self-contracted curves in CAT(0)-spaces and their rectifiability, J. Geom. Anal. 30 (2020), 936-967 (PDF).
  13. Needle decompositions and isoperimetric inequalities in Finsler geometry, J. Math. Soc. Japan 70 (2018), 651-693 (PDF).
  14. Some functional inequalities on non-reversible Finsler manifolds, Proc. Indian Acad. Sci. Math. Sci. 127 (2017), 833-855 (PDF).
    *Corrigendum: 131 (2021), Paper No. 23, 2pp. (PDF).
  15. (with Miklós PÁLFIA)
    Gradient flows and a Trotter-Kato formula of semi-convex functions on CAT(1)-spaces, Amer. J. Math. 139 (2017), 937-965 (PDF).
  16. (K,N)-convexity and the curvature-dimension condition for negative N, J. Geom. Anal. 26 (2016), 2067-2096 (PDF).
  17. (with Miklós PÁLFIA)
    Discrete-time gradient flows and law of large numbers in Alexandrov spaces, Calc. Var. Partial Differential Equations 54 (2015), 1591-1610 (PDF).
  18. Splitting theorems for Finsler manifolds of nonnegative Ricci curvature, J. Reine Angew. Math. 700 (2015), 155-174 (PDF).
  19. (with Kei KONDO & Minoru TANAKA)
    Topology of complete Finsler manifolds with radial flag curvature bounded below, Kyushu J. Math. 68 (2014), 347-357 (PDF).
  20. On the curvature and heat flow on Hamiltonian systems, Anal. Geom. Metr. Spaces 2 (2014), 81-114 (PDF).
  21. Examples of spaces with branching geodesics satisfying the curvature-dimension condition, Bull. Lond. Math. Soc. 46 (2014), 19-25 (PDF).
  22. (with Karl-Theodor STURM)
    Bochner-Weitzenböck formula and Li-Yau estimates on Finsler manifolds, Adv. Math. 252 (2014), 429-448 (PDF).
  23. (with Alexandru KRISTÁLY)
    Caffarelli-Kohn-Nirenberg inequality on metric measure spaces with applications, Math. Ann. 357 (2013), 711-726 (PDF).
  24. Weighted Ricci curvature estimates for Hilbert and Funk geometries, Pacific J. Math. 265 (2013), 185-197 (PDF).
  25. (with Asuka TAKATSU)
    Displacement convexity of generalized relative entropies. II, Comm. Anal. Geom. 21 (2013), 687-785 (PDF).
  26. (with Nicola GIGLI & Kazumasa KUWADA)
    Heat flow on Alexandrov spaces, Comm. Pure Appl. Math. 66 (2013), 307-331 (PDF).
  27. (with Karl-Theodor STURM)
    Non-contraction of heat flow on Minkowski spaces, Arch. Ration. Mech. Anal. 204 (2012), 917-944 (PDF).
  28. (with Nicola GIGLI)
    First variation formula in Wasserstein spaces over compact Alexandrov spaces, Canad. Math. Bull. 55 (2012), 723-735 (PDF).
  29. Barycenters in Alexandrov spaces of curvature bounded below, Adv. Geom. 12 (2012), 571-587 (PDF).
  30. (with Asuka TAKATSU)
    Displacement convexity of generalized relative entropies, Adv. Math. 228 (2011), 1742-1787 (PDF).
  31. Vanishing S-curvature of Randers spaces, Differential Geom. Appl. 29 (2011), 174-178 (PDF).
    *Corrigendum (PDF).
  32. (with Karl-Theodor STURM)
    Heat flow on Finsler manifolds, Comm. Pure Appl. Math. 62 (2009), 1386-1433
    (PDF; minor revisions in Lemma 3.8 & Theorem 3.9).
  33. Finsler interpolation inequalities, Calc. Var. Partial Differential Equations 36 (2009), 211-249 (PDF).
  34. (with Mikaël PICHOT)
    A note on Markov type constants, Arch. Math. (Basel) 92 (2009), 80-88 (PDF).
  35. Uniform convexity and smoothness, and their applications in Finsler geometry, Math. Ann. 343 (2009), 669-699 (PDF).
  36. Extending Lipschitz and Hölder maps between metric spaces, Positivity 13 (2009), 407-425 (PDF).
  37. Gradient flows on Wasserstein spaces over compact Alexandrov spaces, Amer. J. Math. 131 (2009), 475-516 (PDF).
  38. Markov type of Alexandrov spaces of nonnegative curvature, Mathematika 55 (2009), 177-189 (PDF).
  39. (with Kei KONDO)
    Topology of complete manifolds with radial curvature bounded from below, Geom. Funct. Anal. 17 (2007), 1237-1247.
  40. Products, cones, and suspensions of spaces with the measure contraction property, J. Lond. Math. Soc. (2) 76 (2007), 225-236 (PDF).
  41. On the measure contraction property of metric measure spaces, Comment. Math. Helv. 82 (2007), 805-828 (PDF).
  42. Convexities of metric spaces, Geom. Dedicata 125 (2007), 225-250 (PDF).
  43. Reconstructions of distances by energy forms, Proc. Amer. Math. Soc. 134 (2006), 3405-3415.
  44. Regularity of harmonic functions in Cheeger-type Sobolev spaces, Ann. Global Anal. Geom. 26 (2004), 397-410.
  45. Harmonicity of totally geodesic maps into nonpositively curved metric spaces, Manuscripta Math. 114 (2004), 127-138.
  46. Cheeger type Sobolev spaces for metric space targets, Potential Anal. 20 (2004), 149-175.
  47. Totally geodesic maps into metric spaces, Math. Z. 244 (2003), 47-65.

Other publications

  1. Nonlinear geometric analysis on Finsler manifolds, Eur. J. Math. 3 (2017), 916-952 (PDF).
    --A survey on Γ-calculus on Finsler manifolds.
    *Corrigendum (PDF).
  2. Ricci curvature, entropy and optimal transport, London Mathematical Society Lecture Note Series 413 (2014), 145-199 (PDF).
    --Extended lecture notes for Summer School in Grenoble 2009.
  3. Optimal transport and Ricci curvature in Finsler geometry, Adv. Stud. Pure Math. 57 (2010), 323-342 (PDF).
    --A survey article on "Finsler interpolation inequalities" and "Heat flow on Finsler manifolds".
  4. Harmonic maps and totally geodesic maps between metric spaces, Dissertation, Tohoku University, 2003.
    Published in Tohoku Mathematical Publications 28, Tohoku University, 2004.

Articles in Japanese