All issues
Volume 65 (2013)
- Issue 4 Pages 467-
- Issue 3 Pages 313-
- Issue 2 Pages 159-
- Issue 1 Pages 1-
Predecessor
Volume 65, Issue 1
Displaying 1-8 of 8 articles from this issue
- |<
- <
- 1
- >
- >|
-
TADAO ODA2013 Volume 65 Issue 1 Pages 1-30
Published: March 30, 2013
Released on J-STAGE: April 22, 2016
JOURNAL FREE ACCESSConsider 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.View full abstractDownload PDF (466K) -
HITOSHI FURUHATA, TAKASHI KUROSE2013 Volume 65 Issue 1 Pages 31-42
Published: March 30, 2013
Released on J-STAGE: April 22, 2016
JOURNAL FREE ACCESSWe classify the maximal Hessian manifolds of constant Hessaian sectional curvature nonpositive.View full abstractDownload PDF (110K) -
JAIGYOUNG CHOE, JENS HOPPE2013 Volume 65 Issue 1 Pages 43-55
Published: March 30, 2013
Released on J-STAGE: April 22, 2016
JOURNAL FREE ACCESSFor 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 $\boldsymbol{R}^{2k+3}$.View full abstractDownload PDF (112K) -
HAKIM BOUMAZA2013 Volume 65 Issue 1 Pages 57-74
Published: March 30, 2013
Released on J-STAGE: April 22, 2016
JOURNAL FREE ACCESSWe 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.View full abstractDownload PDF (169K) -
ADAM OSȨKOWSKI2013 Volume 65 Issue 1 Pages 75-91
Published: March 30, 2013
Released on J-STAGE: April 22, 2016
JOURNAL FREE ACCESSThe 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.View full abstractDownload PDF (170K) -
OSAMU FUJINO, YASUHIRO ISHITSUKA2013 Volume 65 Issue 1 Pages 93-103
Published: March 30, 2013
Released on J-STAGE: April 22, 2016
JOURNAL FREE ACCESSWe 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.View full abstractDownload PDF (97K) -
ALVARO LIENDO, HENDRIK SÜSS2013 Volume 65 Issue 1 Pages 105-130
Published: March 30, 2013
Released on J-STAGE: April 22, 2016
JOURNAL FREE ACCESSWe 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.View full abstractDownload PDF (260K) -
SHINTARO NAYA, NOBUHIRO INNAMI2013 Volume 65 Issue 1 Pages 131-157
Published: March 30, 2013
Released on J-STAGE: April 22, 2016
JOURNAL FREE ACCESSLet $D$ 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.View full abstractDownload PDF (235K)
- |<
- <
- 1
- >
- >|