Shin-ichi OHTA

Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan

Seminars with E. Milman, 29-30 Sep 2014 (JPN, ENG)
Report of Workshop on Finsler Geometry in Kyoto, 2011 (in Japanese)
Differential Topology Seminar (in Japanese only)

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,
Finsler geometry, the geometry of Banach spaces, ...
Here is my brief curriculum vitae.

Preprints

  1. Needle decompositions and isoperimetric inequalities in Finlser geometry, June 2015 (PDF).
  2. (with Miklós PÁLFIA) Gradient flows and a Trotter-Kato formula of semi-convex functions on CAT(1)-spaces, Oct 2014
    (Revised at 7 Nov 2014: references added; PDF).
  3. (with Miklós PÁLFIA) Discrete-time gradient flows and law of large numbers in Alexandrov spaces, Feb 2014 (Revised at 25 Feb 2015; PDF),
    to appear in Calc. Var. Partial Differential Equations.
  4. (K,N)-convexity and the curvature-dimension condition for negative N, Oct 2013 (Revised at 29 May 2015; PDF),
    to appear in J. Geom. Anal.
  5. (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. Splitting theorems for Finsler manifolds of nonnegative Ricci curvature, J. Reine Angew. Math. 700 (2015), 155-174 (PDF).
  2. (with Kei KONDO & Minoru TANAKA) Topology of complete Finsler manifolds with radial flag curvature bounded below, Kyushu J. Math. 68 (2014), 347-357 (PDF).
  3. On the curvature and heat flow on Hamiltonian systems, Anal. Geom. Metr. Spaces 2 (2014), 81-114 (PDF).
  4. Examples of spaces with branching geodesics satisfying the curvature-dimension condition, Bull. Lond. Math. Soc. 46 (2014), 19-25 (PDF).
  5. (with Karl-Theodor STURM) Bochner-Weitzenböck formula and Li-Yau estimates on Finsler manifolds, Adv. Math. 252 (2014), 429-448 (PDF).
  6. (with Alexandru KRISTÁLY) Caffarelli-Kohn-Nirenberg inequality on metric measure spaces with applications, Math. Ann. 357 (2013), 711-726 (PDF).
  7. Weighted Ricci curvature estimates for Hilbert and Funk geometries, Pacific J. Math. 265 (2013), 185-197 (PDF).
  8. (with Asuka TAKATSU) Displacement convexity of generalized relative entropies. II, Comm. Anal. Geom. 21 (2013), 687-785 (PDF).
  9. (with Nicola GIGLI & Kazumasa KUWADA) Heat flow on Alexandrov spaces, Comm. Pure Appl. Math. 66 (2013), 307-331 (PDF).
  10. (with Karl-Theodor STURM) Non-contraction of heat flow on Minkowski spaces, Arch. Ration. Mech. Anal. 204 (2012), 917-944 (PDF).
  11. (with Nicola GIGLI) First variation formula in Wasserstein spaces over compact Alexandrov spaces, Canad. Math. Bull. 55 (2012), 723-735 (PDF).
  12. Barycenters in Alexandrov spaces of curvature bounded below, Adv. Geom. 12 (2012), 571-587 (PDF).
  13. (with Asuka TAKATSU) Displacement convexity of generalized relative entropies, Adv. Math. 228 (2011), 1742-1787 (PDF).
  14. Vanishing S-curvature of Randers spaces, Differential Geom. Appl. 29 (2011), 174-178 (PDF).
  15. (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).
  16. Finsler interpolation inequalities, Calc. Var. Partial Differential Equations 36 (2009), 211-249 (PDF).
  17. (with Mikaël PICHOT) A note on Markov type constants, Arch. Math. (Basel) 92 (2009), 80-88 (PDF).
  18. Uniform convexity and smoothness, and their applications in Finsler geometry, Math. Ann. 343 (2009), 669-699 (PDF).
  19. Extending Lipschitz and Hölder maps between metric spaces, Positivity 13 (2009), 407-425 (PDF).
  20. Gradient flows on Wasserstein spaces over compact Alexandrov spaces, Amer. J. Math. 131 (2009), 475-516 (PDF).
  21. Markov type of Alexandrov spaces of nonnegative curvature, Mathematika 55 (2009), 177-189 (PDF).
  22. (with Kei KONDO) Topology of complete manifolds with radial curvature bounded from below, Geom. Funct. Anal. 17 (2007), 1237-1247.
  23. Products, cones, and suspensions of spaces with the measure contraction property, J. Lond. Math. Soc. (2) 76 (2007), 225-236 (PDF).
  24. On the measure contraction property of metric measure spaces, Comment. Math. Helv. 82 (2007), 805-828 (PDF).
  25. Convexities of metric spaces, Geom. Dedicata 125 (2007), 225-250 (PDF).
  26. Reconstructions of distances by energy forms, Proc. Amer. Math. Soc. 134 (2006), 3405-3415.
  27. Regularity of harmonic functions in Cheeger-type Sobolev spaces, Ann. Global Anal. Geom. 26 (2004), 397-410.
  28. Harmonicity of totally geodesic maps into nonpositively curved metric spaces, Manuscripta Math. 114 (2004), 127-138.
  29. Cheeger type Sobolev spaces for metric space targets, Potential Anal. 20 (2004), 149-175.
  30. Totally geodesic maps into metric spaces, Math. Z. 244 (2003), 47-65.

Other publications

  1. Harmonic maps and totally geodesic maps between metric spaces, Dissertation, Tohoku University, 2003.
    Published in Tohoku Mathematical Publications 28, Tohoku University, 2004.
  2. Optimal transport and Ricci curvature in Finsler geometry, Adv. Stud. Pure Math. 57 (2010), 323-342 (PDF).
    --Survey article on "Finsler interpolation inequalities" and "Heat flow on Finsler manifolds".
  3. Ricci curvature, entropy and optimal transport (Revised 28 Mar 2014; PDF),
    In: London Mathematical Society Lecture Note Series 413 (2014), 145-199.
    --Extended lecture notes for Summer School in Grenoble 2009.

Articles in Japanese