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Volume And Issue List
Tohoku Mathematical Journal, Second Series
- Vol.65(2013)
  - No.1 p.1-
- Vol.64(2012)
- Vol.63(2011)
- Vol.62(2010)
- Vol.61(2009)
- Vol.60(2008)
- Vol.59(2007)
- Vol.58(2006)
- Vol.57(2005)
- Vol.56(2004)
- Vol.55(2003)
- Vol.54(2002)
- Vol.53(2001)
- Vol.52(2000)
- Vol.51(1999)
- Vol.50(1998)
- Vol.49(1997)
- Vol.48(1996)
- Vol.47(1995)
- Vol.46(1994)
- Vol.45(1993)
- Vol.44(1992)
- Vol.43(1991)
- Vol.42(1990)
- Vol.41(1989)
- Vol.40(1988)
- Vol.39(1987)
- Vol.38(1986)
- Vol.37(1985)
- Vol.36(1984)
- Vol.35(1983)
- Vol.34(1982)
- Vol.33(1981)
- Vol.32(1980)
- Vol.31(1979)
- Vol.30(1978)
- Vol.29(1977)
- Vol.28(1976)
- Vol.27(1975)
- Vol.26(1974)
- Vol.25(1973)
- Vol.24(1972)
- Vol.23(1971)
- Vol.22(1970)
- Vol.21(1969)
- Vol.20(1968)
- Vol.19(1967)
- Vol.18(1966)
- Vol.17(1965)
- Vol.16(1964)
- Vol.15(1963)
- Vol.14(1962)
- Vol.13(1961)
- Vol.12(1960)
- Vol.11(1959)
- Vol.10(1958)
- Vol.9(1957)
- Vol.8(1956)
- Vol.7(1955)
  - No.3 p.141-
  - No.1-2 p.1-
- Vol.6(1954)
  - No.2-3 p.9･･･
  - No.1 p.1-
- Vol.5(1953)
- Vol.4(1952)
- Vol.3(1951)
- Vol.2(1950 - 1951)
- Vol.1(1949 - 1950)

Predecessor

Tohoku Mathematical Journal, First Series

Tohoku Mathematical Journal, Second Series Vol. 65(2013) No. 1

VORONOI TILINGS HIDDEN IN CRYSTALS —THE CASE OF MAXIMAL ABELIAN COVERINGS—

TADAO ODA

Released: April 22, 2016

p.1-30

Consider a finite connected graph possibly with multiple edges and loops. In discrete geometric analysis, Kotani and Sunada constructed the crystal associated to the graph as a standard realization of the maximal abelian covering of the graph. As an application of what the author showed in an earlier paper with Seshadri as a by-product of Geometric Invariant Theory, he shows that the Voronoi tiling (also known as the Wigner-Seitz tiling) is hidden in the crystal, that is, the crystal does not intrude the interiors of the top-dimensional Voronoi cells. The result turns out to be closely related to the tropical Abel-Jacobi map of the associated compact tropical curve.

HESSIAN MANIFOLDS OF NONPOSITIVE CONSTANT HESSIAN SECTIONAL CURVATURE

HITOSHI FURUHATA, TAKASHI KUROSE

Released: April 22, 2016

p.31-42

We classify the maximal Hessian manifolds of constant Hessaian sectional curvature nonpositive.

HIGHER DIMENSIONAL MINIMAL SUBMANIFOLDS GENERALIZING THE CATENOID AND HELICOID

JAIGYOUNG CHOE, JENS HOPPE

Released: April 22, 2016

p.43-55

For each $k$-dimensional complete minimal submanifold $M$ of $\boldsymbol{S}^n$ we construct a $(k+1)$-dimensional complete minimal immersion of $M\times \boldsymbol{R}$ into $\boldsymbol{R}^{n+2}$ and $(k+1)$-dimensional minimal immersions of $M\times \boldsymbol{R}$ into $\boldsymbol{R}^{2n+3}, \boldsymbol{H}^{2n+3}$ and $\boldsymbol{S}^{2n+3}$. Also from the Clifford torus $M=\boldsymbol{S}^k(1/\sqrt{2})\times \boldsymbol{S}^k(1/\sqrt{2})$ we construct a $(2k+2)$-dimensional complete minimal helicoid in $\boldsymbol{R}^{2k+3}$.

LOCALIZATION FOR AN ANDERSON-BERNOULLI MODEL WITH GENERIC INTERACTION POTENTIAL

HAKIM BOUMAZA

Released: April 22, 2016

p.57-74

We present a result of localization for a matrix-valued Anderson-Bernoulli operator acting on the space of $\boldsymbol{C}^N$-valued square-integrable functions, for an arbitrary $N$ larger than 1, whose interaction potential is generic in the real symmetric matrices. For such a generic real symmetric matrix, we construct an explicit interval of energies on which we prove localization, in both spectral and dynamical senses, away from a finite set of critical energies. This construction is based upon the formalism of the Fürstenberg group to which we apply a general criterion of density in semisimple Lie groups. The algebraic nature of the objects we are considering allows us to prove a generic result on the interaction potential and the finiteness of the set of critical energies.

WEIGHTED MAXIMAL INEQUALITIES FOR MARTINGALES

ADAM OSȨKOWSKI

Released: April 22, 2016

p.75-91

The paper contains the study of sharp weighted versions of the classical Doob's weak-type estimates for real-valued martingales. As a by-product, some results concerning the structure of Muckenhoupt's classes are obtained. The proof rests on Bellman function method, i.e., it is based on the construction of a special function having appropriate concavity and majorization properties.

ON THE ACC FOR LENGTHS OF EXTREMAL RAYS

OSAMU FUJINO, YASUHIRO ISHITSUKA

Released: April 22, 2016

p.93-103

We discuss the ascending chain condition for lengths of extremal rays. We prove that the lengths of extremal rays of $n$-dimensional $\boldsymbol{Q}$-factorial toric Fano varieties with Picard number one satisfy the ascending chain condition.

NORMAL SINGULARITIES WITH TORUS ACTIONS

ALVARO LIENDO, HENDRIK SÜSS

Released: April 22, 2016

p.105-130

We propose a method to compute a desingularization of a normal affine variety $X$ endowed with a torus action in terms of a combinatorial description of such a variety due to Altmann and Hausen. This desingularization allows us to study the structure of the singularities of $X$. In particular, we give criteria for $X$ to have only rational, ($\boldsymbol{Q}$-)factorial, or ($\boldsymbol{Q}$-)Gorenstein singularities. We also give partial criteria for $X$ to be Cohen-Macaulay or log-terminal. Finally, we provide a method to construct factorial affine varieties with a torus action. This leads to a full classification of such varieties in the case where the action is of complexity one.

A COMPARISON THEOREM FOR STEINER MINIMUM TREES IN SURFACES WITH CURVATURE BOUNDED BELOW

SHINTARO NAYA, NOBUHIRO INNAMI

Released: April 22, 2016

p.131-157

Let $D$ be a compact polygonal Alexandrov surface with curvature bounded below by $\kappa$. We study the minimum network problem of interconnecting the vertices of the boundary polygon $\partial D$ in $D$. We construct a smooth polygonal surface $\widetilde D$ with constant curvature $\kappa$ such that the length of its minimum spanning trees is equal to that of $D$ and the length of its Steiner minimum trees is less than or equal to $D$'s. As an application we show a comparison theorem of Steiner ratios for polygonal surfaces.

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Volume And Issue List
Tohoku Mathematical Journal, Second Series

Predecessor

Tohoku Mathematical Journal, Second Series Vol. 65(2013) No. 1

VORONOI TILINGS HIDDEN IN CRYSTALS —THE CASE OF MAXIMAL ABELIAN COVERINGS—

HESSIAN MANIFOLDS OF NONPOSITIVE CONSTANT HESSIAN SECTIONAL CURVATURE

HIGHER DIMENSIONAL MINIMAL SUBMANIFOLDS GENERALIZING THE CATENOID AND HELICOID

LOCALIZATION FOR AN ANDERSON-BERNOULLI MODEL WITH GENERIC INTERACTION POTENTIAL

WEIGHTED MAXIMAL INEQUALITIES FOR MARTINGALES

ON THE ACC FOR LENGTHS OF EXTREMAL RAYS

NORMAL SINGULARITIES WITH TORUS ACTIONS

A COMPARISON THEOREM FOR STEINER MINIMUM TREES IN SURFACES WITH CURVATURE BOUNDED BELOW

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Volume And Issue List Tohoku Mathematical Journal, Second Series

Predecessor

Tohoku Mathematical Journal, Second Series Vol. 65(2013) No. 1

System Maintenance

Announcement From J-STAGE

Journal Tools

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Volume And Issue List
Tohoku Mathematical Journal, Second Series