Gabor Toth

Gabor Toth Department of Mathematical Sciences
CV: (PDF file)

Projects and Fields of Interest

  1. Differential Geometry, Harmonic Maps and Minimal Immersions;
  2. Convex Geometry; Measures of symmetry
  3. Middle Egyptian Grammar

Downloadable Manuscripts, Notes, Commentaries, etc.

  1. Notes and Solutions to Problems in Arnold’s Mathematical Methods in Classical Mechanics, Second Edition, Springer, New York, 1989; 46 pages. (Download PDF)
  2. Elements of Real Analysis – History and Foundations; 393 pages. (Download PDFs Part 1 and Part 2)

Publications

Books

  1. Elements of Mathematics – A Problem Centered Approach to History and Foundations, Springer, New York, 2021; Solutions-Manual; Errata and Notes
  2. Measures of Symmetry for Convex Sets and Stability, Springer, New York, 2015
  3. Introduction to Middle Egyptian Grammar through Ancient Writings, Linus Learning, New York, 2013 (ISBN-10: 1-60797-353-7, ISBN-13: 978-1-60797-353-9)
  4. Glimpses of Algebra and Geometry, Second Edition, Springer, New York, 2002 (First Edition, 1997; Japanese translation by Y. Kanie, Springer, Tokyo, 2000); Errata and Notes
  5. Finite Moebius Groups, Spherical Minimal Immersions of Spheres, and Moduli, Springer, New York, 2002;
  6. Glimpses of Algebra and Geometry, Springer, New York, 1998.  Japanese translation of the first edition by Y. Kanie, Springer, Tokyo, 2000.
  7. Harmonic maps and minimal immersions through Representation Theory, Academic Press, Boston, 1990;
  8. Harmonic and Minimal Maps with Applications in Geometry and Physics, Wiley, New York, 1984

Research Articles

  1. (with Q. Guo) Dual mean Minkowski measures and the Grunbaum conjecture for affine diameters, Pacific Journal of Mathematics, 292 (2018), 117–137.
  2. (with K. Miura) On the moduli of isotropic and helical minimal immersions between spheres. Michigan Math. J. 66 (2017), 499-518.
  3. (with Q. Guo) Dual mean Minkowski measures of asymmetry for convex bodies, Sci China Math 59 (2016), DOI 10.1007/s11425-016-5121-x.
  4. On the space of orthogonal multiplications in three and four dimensions and Cayley’s nodal cubic, Contributions to Algebra and Geometry 57 (2016) 407-439, DOI 10.1007/s1336-015-0269-z.
  5. Minimal simplices inscribed in a convex body, Geometriae Dedicata, Vol. 170, 1(2014) 303-318.
  6. Notes on Schneider’s stability estimates for convex sets, J. of Geom. Vol. 104, 3 (2013) 585-598.
  7. Simplicial slices of the space of minimal SU(2)-orbits in spheres, Contributions to Algebra and Geometry, 54(2013) 683-699.
  8. (with M. McClain) The Stela of Qema-Mar and His Household, Journal of Archaeology of the Zagreb Museum, VAMZ, 3. S., XLV (2012) 553-563.
  9. A measure of symmetry for the moduli of spherical minimal immersions, Gemoetriae Dedicata 160, 1(2012) 1-14.
  10. Fine structure of convex sets from asymmetric viewpoint, Contributions to Algebra and Geometry, Col. 52, 1(2011) 171-189.
  11. On the structure of convex sets with symmetries, Geometriae Dedicata, 143 (2009) 69-80
  12. Convex sets with large distortion, J. of Geom. Col 92 (2009) 174-192.
  13. Asymmetry of convex sets with isolated extreme points, Proc. Amer. Math. Soc. Vol 137, No. 1 (2009) 287-295.
  14. On the structure of convex sets with applications to the moduli of spherical minimal immersions, Contributions to Algebra and Geometry, Vol. 49, No. 2 (2008) 491-515.
  15. On the shape of the moduli of spherical minimal immersions, Trans. Amer. Math. Soc., Vol. 358, No.6 (2006) 2425-2446.
  16. Spherical minimal immersions with prescribed codimension, Geometric Dedicata, 113 (2005) 145-163.
  17. Critical points of the distance function on the moduli space for spherical eigenmaps and minimal immersions, Contributions to Algebra and Geometry, Vol. 45, No. 1 (2004) 305-328.
  18. Simplicial intersections of a convex set and moduli for spherical minimal immersions, Michigan Math. Journal, Col. 52 (2004) 341-359.
  19. Moduli for spherical maps and minimal immersions of homogeneous spaces, Journal of Lie Theory, Vol. 12, No. 2 (2002) 551-570.
  20. Operators on moduli for spherical maps of homogeneous spaces, International Journal of Mathematics, Vol. 13, No. 8 (2002) 821-843.
  21. Minimal Immersions of Spheres and Moduli, Period. Math. Hung. 40 (2) (2000) 211-227.
  22. Infinitesimal rotations of isometric minimal immersions between spheres, Amer. J. Math., 122 (2000) 117-152.
  23. (with W. Ziller) Spherical minimal immersions of the 3-sphere, Comment. Math. Helv. 74 (1999) 1-34.
  24. Universal constraints on the range of eigenmaps and spherical minimal immersions, Trans. Amer. Math. Soc. Vol. 351, No. 4 (1999) 1423-1443.
  25. Eigenmaps and the space of minimal immersions between spheres, Indiana Univ. Math. J. Vol. 46, No. 2 (1997) 637-658.
  26. New construction for spherical minimal immersions, Geometric Dedicata, 67 (1997) 187-196.
  27. (with H. Gauchman) Fine structure of the space of spherical minimal immersions, Trans. Amer. Math. Soc. Vol. 348, No.6 (1996) 2441-2463.
  28. (with F. Hiai and D. Petz) Curvature in the geometry of canonical correlations, Studia Sci. Math. Hungar. 32 (1996) 235-249.
  29. (with H. Gauchman) Normed bilinear pairings for semi-Euclidean spaces near the Hurwitz-Radon range, Results in Mathematics, Vol. 30 (1996) 276-301.
  30. On the structure of the moduli space of harmonic eigenmaps, J. Math. Soc. Japan, Vol. 47, No.3 (1995) 503-522.
  31. Quadratic eigenmaps between spheres, Geometric Dedicata, 56 (1995) 35-52.
  32. (with H. Gauchman) Real ortogonal multiplications of codimension two, Nova Journal of Algebra and Geometry, Vol. 3, No.1 (1994) 41-72.
  33. (with H. Gauchman) Constructions of harmonic polynomial maps between spheres, Geometriae Dedicata, 50 (1994) 57-79.
  34. Operators on eigenmaps between spheres, Compositio Mathematica, 88 (1993) 317-332.
  35. Rigidity of minimal submanifolds in terms of higher fundamental forms, Michigan Math. J., Vol. 40, No.3 (1993) 493-505.
  36. (with D. Petz) The Bogoliubov inner product in quantum statistics, Letters in Math. Physics, 27 (1993) 205-216.
  37. Mappings of moduli spaces for harmonic eigenmaps and minimal immersions between spheres, J. Math. Soc. Japan, Vol. 44, No.2 (1992) 179-198.
  38. On the number of rigid minimal immersions between spheres, in ‘The Problem of Plateau’ (Douglas-Rado Memorial Volume) ed. by Th. M. Rassias, World Scientific, Singapore (1992) 327-335.
  39. Moduli spaces of polynomial minimal immersions between complex projective spaces, Michigan Math. J., Vol.37, No.3 (1990) 385-396.
  40. (with D. Barbasch and J. Glazebrook) Harmonic maps between complex projective spaces, Geometriae Dedicata, 33 (1990) 37-50.
  41. (with S.I. Goldberg) Addendum to: Torsion and deformation of contact metric structures on 3-manifolds, Tôhoku Math. J., Vol. 41, No.2 (1989) 259-262.
  42. (with S.I. Goldberg and D. Perrone) Curvature and torsion of contact Riemannian three-manifolds, Proceedings of the Conference in honor of M. DoCarmo, Pitman Press, (1989) 199-210.
  43. Harmonic polynomial maps between spheres and complex projective spaces, in ‘Geometry and Topology’, ed. by G.M. Rassias and G.M. Stratopoulos, World Scientific, Singapore (1989) 306-314.
  44. (with S.I. Goldberg) On closed surfaces immersed in E3 with constant mean curvature, J. London Math. Soc., (2) 38 (1988) 333-340.
  45. (with S.I. Goldberg and D. Perrone) Contact three-manifolds with positive generalized Tanaka-Webster scalar curvature, Comptes Rendus Mathematiques, Acad. Sci. Canada, Vol. X, No.6 (1988) 255-260.
  46. On classification of quadratic harmonic maps of S³, Proc. Amer. Math. Soc., Vol. 102, No.1 (1988) 174-176.
  47. (with S.I. Goldberg and D. Perrone) Curvature of contact Riemannian three-manifolds with critical metrics, III International Symposium on Differential Geometry, Peniscola, Springer Lecture Notes, 1988.
  48. Classification of quadratic harmonic maps of S³ into spheres, Indiana U. Math. J., Col. 36, No.2 (1987) 231-239.
  49. (with F. Kamber and Ph. Tondeur) Transversal Jacobi fields for harmonic foliations, Michigan Math. J., 34 (1987) 261-266.
  50. (with S.I. Goldberg) Torsion and deformation of contact metric structures on 3-manifolds, Tôhoku Math. J., Vol.39, No.3 (1987) 365-372.
  51. On classification of orthogonal multiplications a la DoCarmo-Wallach, Geometriae Dedicata, 22 (1987) 251-254.
  52. (with Ph. Tondeur) On transversal infinitesimal automorphisms for harmonic foliations, Geometriae Dedicata, 24 (1987) 229-236.
  53. (with S.I. Goldberg) Remarks on Wente’s example of an immersed torus in E³, Differential Geometry and its Applications, Proceedings of the Conference, Brno (1986) 71-78.
  54. On nonrigidity of harmonic maps into spheres, Proc. Amer. Math. Soc., Col.94, No.4 (1985) 711-714.
  55. On naturally reductive homogeneous spaces harmonically embedded into spheres, J. London Math. Soc., (2) 29 (1984) 175-180.
  56. Flexible harmonic maps into spheres, in ‘Global Riemannian Geometry’, ed. by T.J. Willmore and N.J. Hitchin, E. Horwood Series, Halsted Press, John Wiley and Sons (1984) 156-167.
  57. (with G. D’Ambra) Parameter space for harmonic maps of constant energy density into spheres, Geometriae Dedicata 17 (1984) 61-67.
  58. (with G. D’Ambra) Extrinsic rigidity for equivariant harmonic maps into spheres, Boll. U.M.I (6) 3-A (1984) 249-255.
  59. (with G. D’Ambra) On infinitesimal and local rigidity of harmonic maps between spheres defined by spherical harmonics, Annali di Mat. (IV) Vol. CXXVI (1984) 25-33
  60. Toroidal Lie group actions on compact Riemannian manifolds and their relations to the fibering problem, Banach Center Publications, Vol. 12, PWN-Polish Sci. Publ. (1984) 233-240.
  61. (with A. Lee) On variation spaces of harmonic maps into spheres, Acta Sci. Math. 46 (1983) 127-141.
  62. Construction des applications harmoniques d’un tore dans la sphère, Annals of Global Analysis and Geometry, Vol. 1, No.2 (1983) 105-118.
  63. Sur les espaces fibrès différentiables munis des groupes de transformations de Lie opérant transversalement aux fibres, Rendiconti di Mat. (1) Vol.2, Series VII (1982) 129-136.
  64. On rigidity of harmonic mappings into spheres, J. London Math. Soc., (2) 26 (1982) 475-486.
  65. Harmonic submersions onto nonnegatively curved manifolds, Acta Math. Acad. Sci. Hungar. 39 (1-3) (1982) 49-53.
  66. On harmonic maps into locally symmetric Riemannian manifolds, in ‘Symposia Mathematica’, Vol. XXVI, Academic Press, New York (1982) 69-94.
  67. On variations of harmonic maps into spaces of constant curvature, Annali di Mat. (IV) Vol. CXXVIII (1981) 389-399.

 

A short novel (in Chinese, PDF File)