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Journal of the Mathematical Society of Japan
- Vol.68(2016)
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Predecessor

Proceedings of the Physico-Mathematical Society of Japan. 3rd Series

Proceedings of the Tokyo Mathematico-Physical Society. 2nd Series

Tokyo Sugaku-Butsurigakukwai Kiji-Gaiyo

Tokyo Sugaku-Butsurigakkwai Hokoku

Tokyo Sugaku-Butsurigaku Kwai Kiji

Tokyo Sugaku Kaisya Zasshi

Journal of the Mathematical Society of Japan Vol. 68(2016) No. 3

Thread construction revisited

Jin-ichi Itoh, Kazuyoshi Kiyohara

Released: July 23, 2016

p.917-938

Staude's thread construction of ellipsoid is revisited from a new view-point concerning the length of geodesic segments. Thanks to the general nature of this view-point, one obtains similar thread construction on other stages, i.e., on “Liouville manifolds”.

The inner boundary of random walk range

Izumi Okada

Released: July 23, 2016

p.939-959

In this paper, we deal with the inner boundary of random walk range, that is, the set of those points in a random walk range which have at least one neighbor site outside the range. If L_n be the number of the inner boundary points of random walk range in the n steps, we prove lim_n→∞ (L_n/n) exists with probability one. Also, we obtain some large deviation result for transient walk. We find that the expectation of the number of the inner boundary points of simple random walk on the two dimensional square lattice is of the same order as n/(log n)².

On an orbifold Hamiltonian structure for the first Painlevé equation

Katsunori Iwasaki, Shu Okada

Released: July 23, 2016

p.961-974

For the first Painlevé equation we establish an orbifold polynomial Hamiltonian structure on the fibration of Okamoto's spaces and show that this geometric structure uniquely recovers the original Painlevé equation, thereby solving a problem posed by K. Takano.

On the topology of projective subspaces in complex Fermat varieties

Alex Degtyarev, Ichiro Shimada

Released: July 23, 2016

p.975-996

Let X be the complex Fermat variety of dimension n = 2d and degree m > 2. We investigate the submodule of the middle homology group of X with integer coefficients generated by the classes of standard d-dimensional subspaces contained in X, and give an algebraic (or rather combinatorial) criterion for the primitivity of this submodule.

Constant mean curvature proper-biharmonic surfaces of constant Gaussian curvature in spheres

Eric Loubeau, Cezar Oniciuc

Released: July 23, 2016

p.997-1024

Constant mean curvature (CMC) surfaces in spheres are investigated under the extra condition of biharmonicity. From the work of Miyata, especially in the flat case, we give a complete description of such immersions and show that for any h ∈ (0,1) there exist CMC proper-biharmonic planes and cylinders in $\mathbb S$⁵ with |H| = h, while a necessary and sufficient condition on h is found for the existence of CMC proper-biharmonic tori in $\mathbb S$⁵.

On the set of fixed points of a polynomial automorphism

Zbigniew Jelonek, Tomasz Lenarcik

Released: July 23, 2016

p.1025-1031

Let $\Bbb K$ be an algebraically closed field of characteristic zero. We say that a polynomial automorphism f: $\Bbb K$ⁿ → $\Bbb K$ⁿ is special if the Jacobian of f is equal to 1. We show that every (n − 1)-dimensional component H of the set Fix(f) of fixed points of a non-trivial special polynomial automorphism f: $\Bbb K$ⁿ → $\Bbb K$ⁿ is uniruled. Moreover, we show that if f is non-special and H is an (n − 1)-dimensional component of the set Fix(f), then H is smooth, irreducible and H = Fix(f). Moreover, for $\Bbb K$ = ℂ if f is non-special and Jac(f) has an infinite order in ℂ^*, then the Euler characteristic of H is equal to 1.

Simple ribbon fusions and genera of links

Kengo Kishimoto, Tetsuo Shibuya, Tatsuya Tsukamoto

Released: July 23, 2016

p.1033-1045

Let K be the result of a 1-fusion (band sum) of a knot k and a distant trivial knot in S³. From results of D. Gabai and of M. G. Scharlemann, we know that the genus of K is at least that of k and that equality holds if and only if the band sum is, in fact, a connected sum (in which case K is ambient isotopic to k). In this paper, we consider a generalization of this result to an m-fusion of a link and a distant trivial link with m-components.

Blanchfield forms and Gordian distance

Maciej Borodzik, Stefan Friedl, Mark Powell

Released: July 23, 2016

p.1047-1080

Given a link in S³ we will use invariants derived from the Alexander module and the Blanchfield pairing to obtain lower bounds on the Gordian distance between links, the unlinking number and various splitting numbers. These lower bounds generalise results recently obtained by Kawauchi.
We give an application restricting the knot types which can arise from a sequence of splitting operations on a link. This allows us to answer a question asked by Colin Adams in 1996.

Reflection principles for ω₂ and the semi-stationary reflection principle

Toshimichi Usuba

Released: July 23, 2016

p.1081-1098

Starting from a model with a weakly compact cardinal, we construct a model in which the weak stationary reflection principle for ω₂ holds but the Fodor-type reflection principle for ω₂ fails. So the stationary reflection principle for ω₂ fails in this model. We also construct a model in which the semi-stationary reflection principle holds but the Fodor-type reflection principle for ω₂ fails.

Parametric Stokes phenomena of the Gauss hypergeometric differential equation with a large parameter

Takashi Aoki, Mika Tanda

Released: July 23, 2016

p.1099-1132

Stokes phenomena with respect to parameters are investigated for the Gauss hypergeometric differential equation with a large parameter. For this purpose, the notion of the Voros coefficient is introduced for the equation. The explicit forms of the Voros coefficients are given as well as their Borel sums. By using them, formulas which describe the Stokes phenomena are obtained.

Jacobian fibrations on the singular K3 surface of discriminant 3

Kazuki Utsumi

Released: July 23, 2016

p.1133-1146

In this paper we give the Weierstrass equations and the generators of Mordell–Weil groups for Jacobian fibrations on the singular K3 surface of discriminant 3.

Minkowski sum of polytopes and its normality

Akihiro Higashitani

Released: July 23, 2016

p.1147-1159

In this paper, we consider the normality or the integer decomposition property (IDP, for short) for Minkowski sums of integral convex polytopes. We discuss some properties on the toric rings associated with Minkowski sums of integral convex polytopes. We also study Minkowski sums of edge polytopes and give a sufficient condition for Minkowski sums of edge polytopes to have IDP.

Generalized commutators of multilinear Calderón–Zygmund type operators

Qingying Xue, Jingquan Yan

Released: July 23, 2016

p.1161-1188

Let T be an m-linear Calderón–Zygmund operator with kernel K and T^* be the maximal operator of T. Let S be a finite subset of Z⁺ × {1,…,m} and denote d$\vec{y}$ = dy₁ … dy_m. Define the commutator T_$\vec{b}$,S of T, and T^*_$\vec{b}$,S of T^* by T_$\vec{b}$,S($\vec{f}$)(x) = ∫_ℝ^nm ∏_(i,j)∈S(b_i(x) − b_i(y_j)) K(x,y₁,…,y_m) ∏_j=1^m f_j(y_j)d$\vec{y}$ and T^*_$\vec{b}$,S($\vec{f}$)(x) = sup_δ>0 | ∫_{∑_j=1^m |x−y_j|² > δ²} ∏_(i,j)∈S(b_i(x) − b_i(y_j))K(x,y₁,…,y_m) ∏_j=1^m f_j(y_j)d$\vec{y}$ |. These commutators are reflexible enough to generalize several kinds of commutators which already existed. We obtain the weighted strong and endpoint estimates for T_$\vec{b}$,S and T^*_$\vec{b}$,S with multiple weights. These results are based on an estimate of the Fefferman–Stein sharp maximal function of the commutators, which is proved in a pretty much more organized way than some known proofs. Similar results for the commutators of vector-valued multilinear Calderón–Zygmund operators are also given.

Non-constant Teichmüller level structures and an application to the Inverse Galois Problem

Kenji Sakugawa

Released: July 23, 2016

p.1189-1218

In this paper, we generalize the Hurwitz space which is defined by Fried and Völklein by replacing constant Teichmüller level structures with non-constant Teichmüller level structures defined by finite étale group schemes. As an application, we give some examples of projective general symplectic groups over finite fields which occur as quotients of the absolute Galois group of the field of rational numbers ℚ.

On framed simple Lie groups

Haruo Minami

Released: July 23, 2016

p.1219-1229

For a compact simple Lie group G, we show that the element [G, ℒ] ∈ π^S_*(S⁰) represented by the pair (G, ℒ) is zero, where ℒ denotes the left invariant framing of G. The proof relies on the method of E. Ossa [Topology, 21 (1982), 315–323].

Indecomposable characters of infinite dimensional groups associated with operator algebras

Takumi Enomoto, Masaki Izumi

Released: July 23, 2016

p.1231-1270

We determine the indecomposable characters of several classes of infinite dimensional groups associated with operator algebras, including the unitary groups of arbitrary unital simple AF algebras and II₁ factors.

On divergence of expectations of the Feynman–Kac type with singular potentials

Yuu Hariya, Kaname Hasegawa

Released: July 23, 2016

p.1271-1296

Motivated by the work of Baras–Goldstein (1984), we discuss when expectations of the Feynman–Kac type with singular potentials are divergent. Underlying processes are Brownian motion and α-stable process. In connection with the work of Ishige–Ishiwata (2012) concerned with the heat equation in the half-space with a singular potential on the boundary, we also discuss the same problem in the half-space for the case of Brownian motion.

Convex functions and barycenter on CAT(1)-spaces of small radii

Takumi Yokota

Released: July 23, 2016

p.1297-1323

We use the convexity of a certain function discovered by W. Kendall on small metric balls in CAT(1)-spaces to show that any probability measure on a complete CAT(1)-space of small radius admits a unique barycenter. We also present various properties of barycenter on those spaces. This extends the results previously known for CAT(0)-spaces and CAT(1)-spaces of small diameter.

Relative Hilbert scheme of points

Iman Setayesh

Released: July 23, 2016

p.1325-1356

Let D be a smooth divisor on a non singular surface S. We compute the Betti numbers of the Hilbert scheme of points of S relative to D. In the case of ℙ² and a line in it, we give an explicit set of generators and relations for the corresponding cohomology groups.

Local maximal operators on fractional Sobolev spaces

Hannes Luiro, Antti V. Vähäkangas

Released: July 23, 2016

p.1357-1368

In this note we establish the boundedness properties of local maximal operators M_G on the fractional Sobolev spaces W^s,p(G) whenever G is an open set in ℝⁿ, 0 < s < 1 and 1 < p < ∞. As an application, we characterize the fractional (s,p)-Hardy inequality on a bounded open set by a Maz'ya-type testing condition localized to Whitney cubes.

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Back Issues

Volume And Issue List
Journal of the Mathematical Society of Japan

Predecessor

Journal of the Mathematical Society of Japan Vol. 68(2016) No. 3

Thread construction revisited

The inner boundary of random walk range

On an orbifold Hamiltonian structure for the first Painlevé equation

On the topology of projective subspaces in complex Fermat varieties

Constant mean curvature proper-biharmonic surfaces of constant Gaussian curvature in spheres

On the set of fixed points of a polynomial automorphism

Simple ribbon fusions and genera of links

Blanchfield forms and Gordian distance

Reflection principles for ω₂ and the semi-stationary reflection principle

Parametric Stokes phenomena of the Gauss hypergeometric differential equation with a large parameter

Jacobian fibrations on the singular K3 surface of discriminant 3

Minkowski sum of polytopes and its normality

Generalized commutators of multilinear Calderón–Zygmund type operators

Non-constant Teichmüller level structures and an application to the Inverse Galois Problem

On framed simple Lie groups

Indecomposable characters of infinite dimensional groups associated with operator algebras

On divergence of expectations of the Feynman–Kac type with singular potentials

Convex functions and barycenter on CAT(1)-spaces of small radii

Relative Hilbert scheme of points

Local maximal operators on fractional Sobolev spaces

System Maintenance

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Volume And Issue List Journal of the Mathematical Society of Japan

Predecessor

Journal of the Mathematical Society of Japan Vol. 68(2016) No. 3

System Maintenance

Announcement From J-STAGE

Journal Tools

Share this Title

Volume And Issue List
Journal of the Mathematical Society of Japan