** Department of Mathematical Sciences**

**CV:** (PDF file)

## Projects and Fields of Interest

- Differential Geometry, Harmonic Maps and Minimal Immersions;
- Convex Geometry; Measures of symmetry
- Middle Egyptian Grammar

## Publications

### Books

*Measures of Symmetry for Convex Sets and Stability*, Springer, New York, 2015*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)*Glimpses of Algebra and Geometry,*Second Edition, Springer, New York, 2002 (First Edition, 1997; Japanese translation by Y. Kanie, Springer, Tokyo, 2000);*Finite Moebius Groups, Spherical Minimal Immersions of Spheres, and Moduli,*Springer, New York, 2002;*Glimpses of Algebra and Geometry,*Springer, New York, 1998. Japanese translation of the first edition by Y. Kanie, Springer, Tokyo, 2000.*Harmonic maps and minimal immersions through Representation Theory,*Academic Press, Boston, 1990;*Harmonic and Minimal Maps with Applications in Geometry and Physics,*Wiley, New York, 1984

### Research Articles

- (with Q. Guo)
*Dual mean Minkowski measures and the Grünbaum conjecture for affine diameters*, Pacific Math. J. (2017) (to appear). - (with K. Miura)
*On the moduli of isotropic and helical minimal immersions between spheres*, Michigan Math. Journal (2017), DOI 10.1307/mmj/1496822425 (to appear) - (with Q. Guo)
*Dual mean Minkowski measures of asymmetry for convex bodies*, Sci China Math 59 (2016) 1383-1394, DOI 10.1007/s11425-016-5121-x - (with K. Miura)
*On the moduli of isotropic and helical minimal immersions between spheres.* - (with Q. Guo)
*Dual mean Minkowski measures and the Grunbaum conjecture for affine diameters.* - (with Q. Guo)
*Dual mean Minkowski measures of asymmetry for convex bodies,*Sci China Math 59 (2016), DOI 10.1007/s11425-016-5121-x. *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.*Minimal simplices inscribed in a convex body,*Geometriae Dedicata, Vol. 170, 1(2014) 303-318.*Notes on Schneider’s stability estimates for convex sets,*J. of Geom. Vol. 104, 3 (2013) 585-598.*Simplicial slices of the space of minimal SU(2)-orbits in spheres,*Contributions to Algebra and Geometry, 54(2013) 683-699.- (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. *A measure of symmetry for the moduli of spherical minimal immersions,*Gemoetriae Dedicata 160, 1(2012) 1-14.*Fine structure of convex sets from asymmetric viewpoint,*Contributions to Algebra and Geometry, Col. 52, 1(2011) 171-189.*On the structure of convex sets with symmetries,*Geometriae Dedicata, 143 (2009) 69-80*Convex sets with large distortion,*J. of Geom. Col 92 (2009) 174-192.*Asymmetry of convex sets with isolated extreme points,*Proc. Amer. Math. Soc. Vol 137, No. 1 (2009) 287-295.*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.*On the shape of the moduli of spherical minimal immersions,*Trans. Amer. Math. Soc., Vol. 358, No.6 (2006) 2425-2446.*Spherical minimal immersions with prescribed codimension,*Geometric Dedicata, 113 (2005) 145-163.*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.*Simplicial intersections of a convex set and moduli for spherical minimal immersions,*Michigan Math. Journal, Col. 52 (2004) 341-359.*Moduli for spherical maps and minimal immersions of homogeneous spaces,*Journal of Lie Theory, Vol. 12, No. 2 (2002) 551-570.*Operators on moduli for spherical maps of homogeneous spaces,*International Journal of Mathematics, Vol. 13, No. 8 (2002) 821-843.*Minimal Immersions of Spheres and Moduli,*Period. Math. Hung. 40 (2) (2000) 211-227.*Infinitesimal rotations of isometric minimal immersions between spheres,*Amer. J. Math., 122 (2000) 117-152.- (with W. Ziller)
*Spherical minimal immersions of the 3-sphere,*Comment. Math. Helv. 74 (1999) 1-34. *Universal constraints on the range of eigenmaps and spherical minimal immersions,*Trans. Amer. Math. Soc. Vol. 351, No. 4 (1999) 1423-1443.*Eigenmaps and the space of minimal immersions between spheres,*Indiana Univ. Math. J. Vol. 46, No. 2 (1997) 637-658.*New construction for spherical minimal immersions,*Geometric Dedicata, 67 (1997) 187-196.- (with H. Gauchman)
*Fine structure of the space of spherical minimal immersions,*Trans. Amer. Math. Soc. Vol. 348, No.6 (1996) 2441-2463. - (with F. Hiai and D. Petz)
*Curvature in the geometry of canonical correlations,*Studia Sci. Math. Hungar. 32 (1996) 235-249. - (with H. Gauchman)
*Normed bilinear pairings for semi-Euclidean spaces near the Hurwitz-Radon range,*Results in Mathematics, Vol. 30 (1996) 276-301. *On the structure of the moduli space of harmonic eigenmaps,*J. Math. Soc. Japan, Vol. 47, No.3 (1995) 503-522.*Quadratic eigenmaps between spheres*, Geometric Dedicata, 56 (1995) 35-52.- (with H. Gauchman)
*Real ortogonal multiplications of codimension two,*Nova Journal of Algebra and Geometry, Vol. 3, No.1 (1994) 41-72. - (with H. Gauchman)
*Constructions of harmonic polynomial maps between spheres,*Geometriae Dedicata, 50 (1994) 57-79. *Operators on eigenmaps between spheres,*Compositio Mathematica, 88 (1993) 317-332.*Rigidity of minimal submanifolds in terms of higher fundamental forms,*Michigan Math. J., Vol. 40, No.3 (1993) 493-505.- (with D. Petz)
*The Bogoliubov inner product in quantum statistics,*Letters in Math. Physics, 27 (1993) 205-216. *Mappings of moduli spaces for harmonic eigenmaps and minimal immersions between spheres,*J. Math. Soc. Japan, Vol. 44, No.2 (1992) 179-198.*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.*Moduli spaces of polynomial minimal immersions between complex projective spaces,*Michigan Math. J., Vol.37, No.3 (1990) 385-396.- (with D. Barbasch and J. Glazebrook)
*Harmonic maps between complex projective spaces,*Geometriae Dedicata, 33 (1990) 37-50. - (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. - (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. *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.- (with S.I. Goldberg)
*On closed surfaces immersed in E3 with constant mean curvature,*J. London Math. Soc., (2) 38 (1988) 333-340. - (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. *On classification of quadratic harmonic maps of S³,*Proc. Amer. Math. Soc., Vol. 102, No.1 (1988) 174-176.- (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. *Classification of quadratic harmonic maps of S³ into spheres*, Indiana U. Math. J., Col. 36, No.2 (1987) 231-239.- (with F. Kamber and Ph. Tondeur)
*Transversal Jacobi fields for harmonic foliations,*Michigan Math. J., 34 (1987) 261-266. - (with S.I. Goldberg)
*Torsion and deformation of contact metric structures on 3-manifolds,*Tôhoku Math. J., Vol.39, No.3 (1987) 365-372*.* *On classification of orthogonal multiplications a la DoCarmo-Wallach,*Geometriae Dedicata, 22 (1987) 251-254.- (with Ph. Tondeur)
*On transversal infinitesimal automorphisms for harmonic foliations,*Geometriae Dedicata, 24 (1987) 229-236. - (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. *On nonrigidity of harmonic maps into spheres,*Proc. Amer. Math. Soc., Col.94, No.4 (1985) 711-714.*On naturally reductive homogeneous spaces harmonically embedded into spheres,*J. London Math. Soc., (2) 29 (1984) 175-180.*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.- (with G. D’Ambra)
*Parameter space for harmonic maps of constant energy density into spheres,*Geometriae Dedicata 17 (1984) 61-67. - (with G. D’Ambra)
*Extrinsic rigidity for equivariant harmonic maps into spheres,*Boll. U.M.I (6) 3-A (1984) 249-255. - (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 *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.- (with A. Lee)
*On variation spaces of harmonic maps into spheres,*Acta Sci. Math. 46 (1983) 127-141. *Construction des applications harmoniques d’un tore dans la sphère,*Annals of Global Analysis and Geometry, Vol. 1, No.2 (1983) 105-118.*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.*On rigidity of harmonic mappings into spheres,*J. London Math. Soc., (2) 26 (1982) 475-486.*Harmonic submersions onto nonnegatively curved manifolds,*Acta Math. Acad. Sci. Hungar. 39 (1-3) (1982) 49-53.*On harmonic maps into locally symmetric Riemannian manifolds,*in ‘Symposia Mathematica’, Vol. XXVI, Academic Press, New York (1982) 69-94.*On variations of harmonic maps into spaces of constant curvature,*Annali di Mat. (IV) Vol. CXXVIII (1981) 389-399.