Shin-ichi OHTA

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

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. Weighted Ricci curvature estimates for Hilbert and Funk geometries, Mar 2012 (PDF).
    --Showing that the weighted Ricci curvature is bounded for Hilbert and Funk geometries with respect to the Lebesgue measure.
  2. Splitting theorems for Finsler manifolds of nonnegative Ricci curvature, Feb 2012 (PDF).
    --Extending the Cheeger-Gromoll splitting theorem to Finsler manifolds by using the weighted Ricci curvature.
  3. (with Asuka TAKATSU) Displacement convexity of generalized relative entropies. II, Dec 2011 (PDF).
  4. (with Karl-Theodor STURM) Bochner-Weitzenböck formula and Li-Yau estimates on Finsler manifolds, Apr 2011 (PDF).
  5. (with Karl-Theodor STURM) Non-contraction of heat flow on Minkowski spaces, Sep 2010 (Revised 18 Apr 2012; PDF),
    to appear in Arch. Ration. Mech. Anal.
    --Heat flow on Minkowski spaces other than inner product spaces is not contractive with respect to the Wasserstein distance.
  6. (with Nicola GIGLI & Kazumasa KUWADA) Heat flow on Alexandrov spaces, Aug 2010 (Revised 19 Jan 2012; PDF),
    to appear in Comm. Pure. Appl. Math.
    --Identifying two interpretations of heat flow, via a Dirichlet form and Wasserstein geometry.
  7. (with Nicola GIGLI) First variation formula in Wasserstein spaces over compact Alexandrov spaces, Jan 2010 (Revised 29 Jul 2010; PDF),
    to appear in Canad. Math. Bull.
    --Generalizing most results in Section 6 of my previous paper "Gradient flows on..." to negative curvature bounds.
  8. Barycenters in Alexandrov spaces of curvature bounded below, Sep 2009 (Revised 30 Dec 2011; PDF),
    to appear in Adv. Geom.

Published papers

(PDF files are of preprint versions, they may be different from published ones.)
  1. (with Asuka TAKATSU) Displacement convexity of generalized relative entropies, Adv. Math. 228 (2011), 1742-1787 (PDF).
  2. Vanishing S-curvature of Randers spaces, Differential Geom. Appl. 29 (2011), 174-178 (PDF).
  3. (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).
  4. Finsler interpolation inequalities, Calc. Var. Partial Differential Equations 36 (2009), 211-249 (PDF).
  5. (with Mikaël PICHOT) A note on Markov type constants, Arch. Math. (Basel) 92 (2009), 80-88 (PDF).
  6. Uniform convexity and smoothness, and their applications in Finsler geometry, Math. Ann. 343 (2009), 669-699 (PDF).
  7. Extending Lipschitz and Hölder maps between metric spaces, Positivity 13 (2009), 407-425 (PDF).
  8. Gradient flows on Wasserstein spaces over compact Alexandrov spaces, Amer. J. Math. 131 (2009), 475-516 (PDF).
  9. Markov type of Alexandrov spaces of nonnegative curvature, Mathematika 55 (2009), 177-189 (PDF).
  10. (with Kei KONDO) Topology of complete manifolds with radial curvature bounded from below, Geom. Funct. Anal. 17 (2007), 1237-1247.
  11. Products, cones, and suspensions of spaces with the measure contraction property, J. Lond. Math. Soc. (2) 76 (2007), 225-236 (PDF).
  12. On the measure contraction property of metric measure spaces, Comment. Math. Helv. 82 (2007), 805-828 (PDF).
  13. Convexities of metric spaces, Geom. Dedicata 125 (2007), 225-250 (PDF).
  14. Reconstructions of distances by energy forms, Proc. Amer. Math. Soc. 134 (2006), 3405-3415.
  15. Regularity of harmonic functions in Cheeger-type Sobolev spaces, Ann. Global Anal. Geom. 26 (2004), 397-410.
  16. Harmonicity of totally geodesic maps into nonpositively curved metric spaces, Manuscripta Math. 114 (2004), 127-138.
  17. Cheeger type Sobolev spaces for metric space targets, Potential Anal. 20 (2004), 149-175.
  18. 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 1 Jul 2010; PDF), to appear in Séminaires et Congrès.
    --Extended lecture notes for Summer School in Grenoble 2009.

Articles in Japanese