Publications

Papers

1. Magnitude function identifies generic finite metric space, to appear in Discrete Analysis, arXiv:2401.00786

2. Residues of manifolds, J. Geom. Anal. 33, 357 (2023), 1-68, DOI:10.1007/s12220-023-01393-9, arXiv:2012.01713

3. Uniqueness of centers of nearly spherical bodies, Mathematika 68 (2022), 1268-1291, DOI:10.1112/mtk.12166, arXiv:2103.07685 

4. (with Shigehiro Sakata) Strict power concavity of a convolution, Ann. Mat. Pura Appl. 201 (2022), 1553-1575, DOI:10.1007/s10231-021-01170-x, arXiv:2005.00230

5. Self-repulsiveness of energies for closed submanifolds, Math. Nachr. 296 (2023 Feb), 797-810, DOI: 10.1002/mana.202000158,  arXiv:2004.02351.

6. (with Remi Langevin and Jean-Claude Sifre) Osculating spheres to a family of curves, Saitama Math. J. 33 (2021), 13-22.

7. Pompeiu's theorem and the moduli space of triangles, Results in Math. 75 Article number: 145 (2020)  12pp., DOI: 10.1007/s00025-020-01271-8 arXiv:2002.07084

8. Möbius invariant metrics on the space of knots, Geom. Dedicata 209 (2020), 1-13, DOI: 10.1007/s10711-020-00518-6 arXiv 1905.06098

9. (with Gil Solanes) Erratum to Regularized Riesz energies of submanifolds, Math. Nachr. 293 (2020), 1014-1019, DOI: 10.1002/mana.202000024

10. Regularization of Neumann and Weber formulae for inductance, Journal of Geometry and Physics 149 (2020), 103567, 12pp., DOI: 10.1016/j.geomphys.2019.103567, arXiv 1804.11098

11. Characterization of balls by generalized Riesz energy, Math. Nachr. 292 (2019), 159-169, DOI: 10.1002/mana.201700256,  arXiv:1707.02405

12. (with Gil Solanes)  Regularized Riesz energies of submanifolds, Math. Nachr. 291 (2018), 1356-1373, DOI: 10.1002/mana.201600083 , arXiv:1512.07935, one hour presentation file

13. (with Kentaro Mikami and Kunio Sugahara) Triangles with sides in arithmetic progression, Elem. Math. 72 (2017) 75-79. DOI: 10.4171/EM/327

14. (with Gil Solanes) Möbius invariant energies and average linking with circles, Tohoku Math. J. 67 (2015),   51-82 arXiv:1010.3764, one hour presentation file

15. Minimal unfolded regions of a convex hull and parallel bodies, Hokkaido Math. J.  44 (2015), 175-183  arXiv:1205.0662

16. Measure of a 2-component link, Tohoku Math. J. 65 (2013), 427-440 arXiv:0709.2215

17. (with Remi Langevin and Shigehiro Sakata) Application of spaces of subspheres to conformal invariants of curves and canal surfaces, Ann. Polon. Math. 108 (2013), 109-131 DOI: 10.4064/ap108-2-1 arXiv:1102.0344

18. The configuration space of equilateral and equiangular hexagons, Osaka J. Math. 50, (2013), 477-489, arXiv:1105.5046 Gif movies of equilateral and equiangular hexagons, one hour presentation file

19. Isoperimetric characterization of the incenter of a triangle, Elem. Math. 68 (2013), 78-82. doi: 10.4171/EM/223  arXiv:1012.5918

20. (with Udo Hertrich-Jeromin and Alastair King) On the Möbius geometry of Euclidean triangles, Elemente der Mathematik 68 (2013), 96-114.

21. Renormalization of potentials and generalized centers, Adv. Appl. Math. 48 (2012), 365-392, arXiv:1008.2731 ;         Corrigendum to ``Renormalization of potentials and generalized centers'' [Adv. in Appl. Math. 48 (2) (2012) 365-392], Adv. in Appl. Math. 49 (2012) 397-398 (replacement of a graph of a potential), one hour presentation file

22. (with Remi Langevin) Conformal invariance of the writhe of a knot, J. Knot Theory Ramifications 19 (2010) 1115-1123, arXiv:0803.1876

23. (with Remi Langevin) Conformal arc-length as 1/2-dimensional length of the set of osculating circles, Comm. Math. Helv. 85 (2010) 273-312 arXiv:0803.1060

24. The configuration space of planar spidery linkages, Topology Appl. 154 (2007), 502-526. arXive. 

25. (with R. Langevin) Conformally invariant energies of knots, J. Institut Math. Jussieu 4 (2005), 219-280. arXive, abstract, one hour presentation file

26. Energy funcitonals of knots II, Topology Appl. 56 (1994), 45-61

27.  Family of energy functionals of knots, Topology Appl. 48 (1992), 147-161

28.  Energy of a knot, Topology 30 (1991), 241-247                  

Proceedings

29. (with H. Funaba) Möbius invariant energy of tori of revolution, Journal of Physics: Conference Series, Volume 544, Issue 1, article id. 012019 (2014) arXiv:1305.3682

30. Ideal, best packing, and energy minimizing double helices, Progress of Theoretical Physics Supplement 191 (2011) 215-224, arXiv:1104.0489, one hour presentation file

31. Energy of knots and the infinitesimal cross ratio, Proceedings of the Conference "Groups, Homotopy and Configuration Spaces", Geometry and Topology Monographs 13(2008) 421-445.

32. The configuration space of a spider. Intelligence of low dimensional topology 2006, 245–252, Ser. Knots Everything, 40, World Sci. Publ., Hackensack, NJ, 2007. 

33. A Note on Y-energies of Knots, OCAMI Studies Vol 1 (1). Knot Th eory for Scientific Objects, proceedings of the International Workshop on Knot Theory for Scientific Objects (2007) 85-95. arXive.

34. (with Remi Langevin) Conformally geometric viewpoints for knots and links I, in Physical Knots: Knotting, Linking, and Folding Geometric Objects in R^3, AMS Special Session on Physical Knotting and Unknottin, Las Vegas, Nevada, April 21-22, 2001, J. A. Calvo, K. Millett, and E. Rawdon eds., Contemp. Math. 304, Amer. Math. Soc., Providence, RI, (2002), 187-194.

35. Asymptotic behavior of energies of polygonal knots, Proceedings of the Conference on Low Dimensional Topology, H. Nencka and R. Vasconcelos eds., Contemporary Mathematics (CONM) book series, Amer. Math. Soc., 1999, 235-249

36. Energy of knots in a 3-manifold; The spherical and the hyperbolic cases, Proceedings of Knots '96, S. Suzuki ed., World Scientific, 1997, 449-464

37. Energy functionals of knots, in "Topology -Hawaii", K.H. Dovermann ed., World Scientific, Singapore, (1992), 201-214

Survey articles

38. Energy of knots, "Ideal Knots", A. Stasiak, V. Katrich, L. H. Kauffman eds., World Scientific, 1998, 288-314

39. Energy of knots, Sugaku Expositions 13 ,2000, 73-90

Book (2nd edition in progress):

• Energy of knots and conformal geometry. Series on Knots and Everything Vol. 33, World Scientific, Singapore, 304 pages. ISBN 981-238-316-6, 2003, Errata updated Sept. 2018

Monograph in progress:

• (with R. Langevin) Extrinsic conformal geometry - with applications to curves, surfaces and foliations -

Preprints:

• 1. Magnitude function identifies generic finite metric space, arXiv:2401.00786

  2. Equisectional equivalence of triangles,  arXiv:1608.08087  -> Some of the content has been carried forward into ``Pompeiu's theorem and the moduli space of triangle'' in Results in Math.

  3. Uniqueness of radial centers of parallel bodies arXiv:1109.5069 -> Some of the content has been carried forward into ``Uniqueness of centers of nearly spherical bodies'' in Mathematika.

Miscellaneous:

• Conformal dual of a quadruplet of points, arXiv:0709.0454. This paper has been published by a predatory journal which does not appear in MathSciNet. I regret that I did not have knowledge of predatory publishers at that time. 

日本語：

結び目のエネルギー, 数学 Vol. 49 (1997) No. 4,  365-378