Welcome!!

English version / Japanese version

E-mail :

kfunano[[at]]tohoku.ac.jp, yahoonitaikou[[at]]gmail.com

(Feel free to email me)

Postal address:

Division of Mathematics &

Research Center for Pure and Applied Mathematics

Graduate School of Information Sciences

Tohoku University

6-3-09 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan link

Here is my brief curriculum vitae.

- Reseach interests

Concentration of measure, Spectral geometry, Convex geometry, and their related topics.

- Papers and preprints

1. In preparation.
2. (With L. Cavallina, A. Henrot, A. Lemenant, I. Lucardesi, and S. Sakaguchi) Two extremum problems for Neumann eigenvalues, preprint. link (Here is a related slide)
3. A universal inequality for Neumann eigenvalues of the Laplacian on a convex domain in Euclidean space, Canad. Math. Bull. 67 (2024), no. 1, 222–226.
4. A note on domain monotonicity for the Neumann eigenvalues of the Laplacian, Illinois J. Math. 67 (2023), no. 4, 677–686.
5. (With Y. Sakurai) Upper bounds for higher order Poincaré constants, Trans. Amer. Math. Soc. 373 (2020), no. 6, 4415–4436. link
6. (With Y. Sakurai) Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold, Proc. Amer. Math. Soc. 147 (2019), no. 7, 3155–3164. link
7. (With H. Alpert) Macroscopic scalar curvature and areas of cycles. Geom. Funct. Anal. 27 (2017), no. 4, 727–743. link
8. Applications of the `ham sandwich theorem' to eigenvalues of the Laplacian. Anal. Geom. Metr. Spaces 4 (2016), 317–325. link
9. Estimates of eigenvalues of the Laplacian by a reduced number of subsets. Israel J. Math. 217 (2017), no. 1, 413–433. link.
10. Eigenvalues of Laplacian and multi-way isoperimetric constants on weighted Riemannian manifolds, preprint. pdf (Revised at 21th June 2015. A new problem has been added)
11. (With T. Shioya) Concentration, Ricci curvature, and eigenvalues of Laplacian. Geom. Funct. Anal. 23 (2013), no. 3, 888–936. link
12. Two infinite versions of the nonlinear Dvoretzky Theorem, Pacific J. Math. 259 (2012), no. 1, 101–108. link
13. Observable concentration of mm-spaces into Hadamard manifolds, preprint. pdf
14. Rate of convergence of stochastic processes with values in R-trees and Hadamard manifolds. Osaka J. Math. 47 (2010), no. 4, 911–920. link.
15. Concentration of maps and group actions. Geom. Dedicata 149 (2010), 103–119. link.
16. Exponential and Gaussian concentration of 1-Lipschitz maps. Manuscripta Math. 130 (2009), no. 3, 273--285. link
17. Central and $L_p$-concentration of 1-Lipschitz maps into $R$-trees. J. Math. Soc. Japan 61 (2009), no. 2, 483--506. link
18. Concentration of 1-Lipschitz maps into an infinite dimensional $\ell_p$-ball with the $\ell_q$-distance function. Proc. Amer. Math. Soc. 137 (2009), no. 7, 2407--2417. link
19. Estimates of Gromov's box distance. Proc. Amer. Math. Soc. 136 (2008), no. 8, 2911--2920. link
20. Observable concentration of mm-spaces into spaces with doubling measures. Geom. Dedicata 127 (2007), 49--56. link

Here is a list of my papers in MathSciNet. Most preprints can be found here on the arXiv.

- Other articles

1. Some universal inequalities of eigenvalues and upper bounds for the $L_{\infty}$ norm of eigenfunctions of the Laplacian (survey article) pdf
2. Book Review “Introduction to coarse geometry (by Tomohiro Fukaya)” (in japanese), Mathematical Sciences, SAIENSU-SHA Co.,Ltd, Jun. 2020. Link
3. Upper bounds for higher-order Poincar.\'e constants, RIMS kokyuroku No. 2172 (survey article) Link
4. Ramsey type theorems in geometry (in japanese), Mathematical Sciences, SAIENSU-SHA Co.,Ltd, Dec. 2016. Link

A Photo taken at Cat Island (Tashiro Island)