## プレプリント

• Analytic extension of exceptional constant mean curvature one elliptic catenoids in de Sitter 3-space,

## 出版予定

• Analytic extension of Jorge-Meeks type maximal surfaces in Lorentz-Minkowski 3-space ,
preprint, arXiv:1509.05853 (19 Sept. 2015) , to appear in Osaka Journal of Mathematics.

## 出版済論文

• Mixed type surfaces with bounded mean curvature in 3-dimensional space-times,
Differential Geometry and Its Applications, vol. 52 (2017), 64--77.
http://dx.doi.org/10.1016/j.difgeo.2017.03.009
• An index formula for hypersurfaces which admit only generic corank one singularities
Jurnal of Mathematical Society of Japan, vol. 69 No. 1 (2017) 417--457.
doi: 10.2969/jmsj/06910417
• Entire zero mean curvature graphs of mixed type in Lorentz-Minkowski 3-space
The Quaterly Journal of Mathematics, doi:10.1093/qmath/haw038
• Isometric deformations of cuspidal edges
Tohoku Mathematical Journal (2), vol. 68, Number 1 (2016), 73--90.
https://projecteuclid.org/euclid.tmj/1458248863
• Behavior of Gaussian curvature near non-degenerate singular points on wave fronts
in "Geometry and Topology of Manifolds", A. Futaki et. al. ed., pages 247--281, Springer Proceedings in Mathematics & Statistics, volume 154, 2016.
DOI 10.1007/978-4-431-56021-0_14
• Intrinsic properties of surfaces with singularities
International Journal of Mathematics, Vol. 26, No. 4 (2015) 1540008 (34 pages),
DOI: 10.1142/S0129167X1540008X.
• Zero mean curvature surfaces in Lorentz-Minkowki 3-space which change type across a light-like line
Osaka Journal of Mathematics, volue 52 (2015), 285--297.
http://projecteuclid.org/euclid.ojm/1427202882
Erratum to the article "Zero mean curvature surfaces in Lorentz-Minkowki 3-space which change type across a light-like line"
Osaka Journal of Mathematics, volue 53 (2016), 289--293.
• Zero mean curvature surfaces in Lorentz-Minkowski 3-space and 2-dimensional fluid mechanics
• A duality for conformally flat hypersurfaces
Beiträge zur Algebra und Geometrie/ Contribution to Algebra and Geometry, 2014, DOI 10.1007/s13366-014-0225-3.
• Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space
Michigan Mathematical Journal, volume 63, 2014, 189--207.
• Intrinsic invariants of cross caps
Selecta Mathematica, volume 20, Issue 3 (2014), 769--785
• Flat surfaces in hyperbolic 3-space whose hyperbolic Gauss maps are bounded
Revista Matemática Iberoamericana, 30 (2014), 309--316.
• A construction of a complete bounded null curve in C3
Kodai Mathematical Journal, 37 (2014), 59--96.
• Hyperbolic metrics on Riemann surfaces and space-like CMC-1 Surfaces in de Sitter 3-Space
in "Recent Trends in Lorentzian Geometry", M. Sánchez et al. (eds.), Springer Proceedings in Mathematics & Statistics 26, pages 1--47, 2013.
• Zero mean curvature surfaces in L3 containing a light-like line
• Coherent tangent bundles and Gauss-Bonnet formulas for wave fronts
• CMC-1 trinoids in H3 and metrics of constant curvature one with conical singularities on S2,
Proceedings of Japan Academy, vol. 87, Ser. A (2011), 144--149.
• A2-singularities of hypersurfaces with non-negative sectional curvature in Euclidean space
• Applications of a completeness lemma in minimal surface theory to various classes of surfaces
Bulletin of the London Mathematical Society, vol. 43 (2011), 191--199.
Corrigendum: Applications of a completeness lemma in minimal surface theory to various classes of surfaces
Bulletin of the London Mathematical Society, vol. 44 (2012), 617--618.
• The duality of conformally flat manifolds
Bulletin of the Brasilian Mathematical Society (N. S.), vol. 42 (2011), 131--152.
• The duality between singular points and inflection points on wave fronts,
• Singularities of Blaschke normal maps of convex surfaces
• New maximal surfaces in Minkowski 3-space with arbitrary genus and their cousins in de Sitter 3-space
• Spacelike mean curvature one surfaces in de Sitter 3-space,
• Complete bounded holomorphic curves immersed in C2 with arbitrary genus,
• Complete bounded null curves immersed in C3 and SL(2,C),
Erratum to: Complete bounded null curves immersed in C3 and SL(2,C),
A construction of a complete bounded null curve in C3,
preprint, math.DG/0603530 (Version 7; 02 Jan, 2013)
• Asymptotic behavior of flat surfaces in hyperbolic 3-space,
• Ak singularities of wave fronts,
• The geometry of fronts,
• Behavior of corank one singular points on wave fronts,
• Hyperbolic Schwarz map for the hypergeometric differential equation,
• Derived Schwarz map of the hypergeometric differential equation and a parallel family of flat fronts,
• Confluence of swallowtail singularities of the hyperbolic Schwarz map defined by the hypergeometric differential equation,
• Singularities of maximal surfaces,
• Flat fronts in hyperbolic 3-space and their caustics,
• Maximal surfaces with singularities in Minkowski space,
• Singularities of flat fronts in hyperbolic 3-space,
• Constructing mean curvature 1 surfaces in H3 with irregular ends,
in "Global theory of minimal surfaces", pp. 561--584, Clay Math. Proc., 2, Amer. Math. Soc., 2005.
• Flat fronts in hyperbolic 3-space,
• Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature I,
• An elementary proof of Small's formula for null curves in PSL(2,C) and an analogue for Legendrian curves in PSL(2,C),
• Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature II,
• Minimal surfaces that attain equality in the Chern-Osserman inequality
in "Differential Geometry and Integrable Systems", Ed. M. Guest, R. Miyaoka and Y. Ohnita, Contemporary Mathematics 308, American Mathematical Society, 2002, pp. 223-228.
• An analogue of minimal surface theory in SL(n,C)/SU(n),
• Metrics of constant curvature 1 with three conical singularities on 2-sphere,
Illinois Journal of Mathematics, vol. 44 (2000), 72--94.
• General existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux,
Communications in Analysis and Geometry, vol. 8 (2000), 83--114.
• Flux for mean curvature 1 surfaces in hyperbolic 3-space, and applications,
• An inverse problem of the flux for minimal surfaces,
• Irreducible constant mean curvature 1 surfaces in hyperbolic space with positive genus,
Tôhoku Mathematical Journal, vol. 49 (1997), 449--484.
• General existence of minimal surfaces with prescribed flux II,
in "Topics in Complex Analysys, Differential Geometry and Mathematical Physics", (ed. S. Dimiev et. al),
World Scientific (1997), 116--135.
• A duality on CMC-1surface in the hyperbolic 3-space and a hyperbolic analogue of the Osserman Inequality,
Tsukuba Journal of Mathematics, vol. 21 (1997), 229--237.
• Another construction of a CMC-1 surface in H3,
Kyungpook Mathematical Journal, vol. 35 (1996), 831--849.
• Surfaces of constant mean curvature c in H3(-c2) with prescribed hyperbolic Gauss map,
Mathematische Annalen, vol. 304 (1996), 203--224.
• Deformation of Lie groups and their application to surface theory,
in "Geometry and Its Applications" (ed. by T. Nagano et al.), World Scientific (1993), 241--255.
• Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space,
Annals of Mathematics, vol. 137 (1993), 611--638.
• A parametrization of the Weierstrass formulae and perturbation of some complete minimal surfaces of R3 into the hyperbolic 3-space,
Journal für reine und angewandte Mathematik, vol. 432 (1992), 93--116.
• A deformation of tori with constant mean curvature in R3 to those in other space forms,
Transactions of the American Mathematical Society, vol. 330 (1992), 845--857.
• Deformations of symmetric spaces of compact type to their concompact duals,
Japanese Journal of Mathematics, vol. 17 (1991), 383--399.
• Harmonic non-holomorphic maps of 2-tori into the 2-sphere,
in "Geometry of Manifolds" (ed. by K. Shiohama), Academic Press (1989), pp. 151--160.
• Complete space-like surfaces with constant mean curvature in the Minkowski 3-space,
Tokyo Journal of Mathematics, vol. 11 (1988), 329--338.
• Minimal tori in S3 whose lines of curvature lie in S2,
Tokyo Journal of Mathematics, vol. 10 (1987), 215--226.

## 総論・解説

• Period problems for mean curvature one surfaces in H3 (with applications to surfaces of a low total curvature),
Advanced Studies in Pure Mathemaatics, {\bf 51} (2008), {\sc Surveys on Gemetry and Integrable Systems}, pp. 347--399.
• 3次元双曲型空間における平坦な曲面
Flat fronts in the hyperbolic 3-space (Japanese),
「部分多様体の微分幾何学およびその周辺領域の研究」 数理解析研究所講究録 1236, 2001年11月, pp. 49--59.
"Geometry of submanifolds and related topics" (Japanese) (Kyoto, 2001). Sūrikaisekikenkyūsho Kōkyūroku No. 1236 (2001), 49--59.
• 双曲型空間の平均曲率 1をもつ曲面の全曲率
Total curvature of mean curvature 1 surfaces in a hyperbolic space, (Japanese)
「部分多様体の幾何学」 数理解析研究所講究録 1206, 2001年5月, pp. 134--143.
"Geometry of submanifolds"(Japanese) (Kyoto, 2001), Sūrikaisekikenkyūsho Kōkyūroku No. 1206 (2001), 134--143.
• Mean curvature 1 surfaces with low total curvature in hyperbolic 3-space,
Advanced Studies in Pure Mathematics 29, 2000, "Minimal surfaces, Geometric Analysis and Symplictic Geometry", pp. 279--297.
• An inverse problem of the flux formula,
in "Proceedings of the 4th International Congress of Geometry (Thessaloniki, 1996)", 228--233,
Giachoudis-Giapoulis, Thessaloniki, 1997.
• 3次元双曲型空間の平均曲率1の曲面の幾何
Geometry of surfaces of constant mean curvature 1 in the hyperbolic 3-space,
数学 47 (1995), 145--157
Sugaku Expositions, vol.10 (1997), 41--55 (translated by the authors from Japanese).
• 3次元双曲型空間内の平均曲率1の曲面の双対性とその応用
Duality of surfaces of mean curvature 1 in 3-dimensional hyperbolic spaces and its applications. (Japanese)
「部分多様体論とその周辺」 数理解析研究所講究録 907, 1995年5月, pp. 1--11.
"Geometry of submanifolds and related topics" (Japanese) (Kyoto, 1995). Sūrikaisekikenkyūsho Kōkyūroku No. 907 (1995), 1--11.
• Surfaces of constant mean curvature-1 in the hyperbolic 3-space,
Geometry and global analysis (Sendai, 1993), 399--411, Tohoku Univ., Sendai, 1993.