Hokkaido Mathematical Journal

No. 2

MORIYA, Katsuhiro;

Parametrizations of minimal timelike surfaces in the four-dimensional pseudo-Euclidean space of index two.

Hokkaido Mathematical Journal, 55 (2026) pp.167-181

Fulltext

PDF

Abstract

We construct representation formulas for local null curves in the four-dimensional pseudo-Euclidean space of index two and derive corresponding parametrizations for local minimal timelike surfaces without integration. As a special case of the representation formula, we construct a representation formula for local null curves in the three-dimensional pseudo-Euclidean space of index one that involves integration. Our results provide examples of minimal timelike surfaces.

Keywords	timelike surfaces; minimal surfaces; parametrizations;
msc2020(primary)	53B30; 53C42; 53A07;

KASUGA, Kazuhiro;

Norm of the composition operator from Bloch space to Bergman space II.

Hokkaido Mathematical Journal, 55 (2026) pp.183-191

Fulltext

PDF

Abstract

In this paper, we study some quantity equivalent to the norm of Bloch to $A^{p}_{\alpha}$ composition operator on one condition, where 'Bloch' is the Bloch space on the unit ball of $\mathbb{C}^m$, $A^{p}_{\alpha}$ is the weighted Bergman space on the unit ball of $\mathbb{C}^n$, ($0 < p <\infty$ and $-1 < \alpha < \infty$).

Keywords	composition operator; Bloch space; Bergman space;
msc2020(primary)	32A10; 32A18; 32A36;

RAFAEL, F. S.;

Determinants on odd-dimensional projective spaces.

Hokkaido Mathematical Journal, 55 (2026) pp.193-227

Fulltext

PDF

Abstract

We establish formulae for the regularized determinant of the Laplacian and twisted Laplacian on odd-dimensional real projective spaces. This work corresponds to a generalization of the previous formulae for this type of space and we prove the equivalence in the common cases, what leads to interesting, if simple, identities involving special values of Bernoulli polynomials and the Riemann zeta function. As application, we calculate the analytic torsion of these spaces in relation to all unitary representations of their fundamental group and obtain an expression relating it to the volume of the manifold.

Keywords	Regularized determinants; projective spacesm; Bernoulli polynomials; Riemann zeta function; analytic torsion;
msc2020(primary)	11M36; 11B68; 11M06; 58J52; 58J50;

MENDES, Luís Gustavo; PUCHURI, Liliana;

Effective Integrability of Lins Neto's Family of Foliations.

Hokkaido Mathematical Journal, 55 (2026) pp.229-255

Fulltext

PDF

Abstract

A. Lins Neto presented in [LN02] a $1$-dimensional family of degree four foliations on the complex projective plane $\mathcal{F}_{t \in \overline{\mathbb{C}}}$ with non-degenerate singularities of fixed analytic type, whose set of parameters $t$ for which $\mathcal{F}_t$ is an elliptic pencil is dense and countable. In [Mc01] and [Gu02], M. McQuillan and A. Guillot showed that the family lifts to linear foliations on the abelian surface $E \times E$, where $E = \mathbb{C}/\Gamma$, $\Gamma = \langle 1 , \tau \rangle$ and $\tau$ is a primitive 3rd root of unity. The parameters for which $\mathcal{F}_t$ are elliptic pencils being $t\in \mathbb{Q}(\tau) \cup {\infty}$, in [Pu13] the second author gave a closed formula for the degree of the elliptic curves of $\mathcal{F}_t$ as function of $t \in \mathbb{Q}(\tau)$. In this work we determine degree, positions and multiplicities of singularities of the elliptic curves of $\mathcal{F}_ t$, for any given $t \in \mathbb{Z}(\tau)$, algorithmically implemented in Python. And also we obtain the explicit expressions for the generators of the elliptic pencils, using the Singular software. Our constructions depend on the effect of quadratic Cremona maps on the family of foliations $\mathcal{F}_t$.

Keywords	Birational automorphisms; elliptic surfaces; singularities of holomorphic foliations;
msc2020(primary)	14E07; 14J27; 32M25; 32S65;

LATERVEER, Robert;

Variation on a theme of Beauville-Voisin.

Hokkaido Mathematical Journal, 55 (2026) pp.257-265

Fulltext

PDF

Abstract

The Beauville-Voisin conjecture is about the Chow ring of hyper-Kähler varieties. We consider a variant version taking place in the ring of algebraic cycles modulo algebraic equivalence. We prove this variant version is true in codimension at least 3 for Fano varieties of lines on cubic fourfolds, and for double EPW sextics.

Keywords	Chow groups; motives; hyper-Kähler varieties; Beauville-Voisin conjecture; Beauville "splitting property" conjecture;
msc2020(primary)	14C15; 14C25; 14C30; 14J42;

MAKHMUTOV, Shamil; RÄTTYÄ, Jouni;

Integral estimates related to analytic self-maps and Dirichlet classes via hyperbolic oscillation.

Hokkaido Mathematical Journal, 55 (2026) pp.267-282

Fulltext

PDF

Abstract

It is shown that the growth of the hyperbolic derivative of an analytic self-map $\varphi$ of the unit disc naturally restricts the behaviour of its modulus yielding new integral growth estimates for $z\mapsto \log\frac{1-|\varphi(0)|^2}{1-|\varphi(z)|^2}$. Moreover, Hörmander-type maximal function is used to derive a kind of embedding theorem involving hyperbolic derivative. This result is further used to characterize weighted hyperbolic Dirichlet classes in terms of hyperbolic oscillation. Certain inclusion relations related to hyperbolic Besov classes are also briefly discussed.

Keywords	bounded analytic function; hyperbolic derivative; hyperbolic metric; Hörmander-type maximal function; doubling weight;
msc2020(primary)	30H05;
msc2020(secondary)	30H20; 30H25; 30A10;

TOMIOKA, Shunsuke;

An Inverse Theorem for the Perron-Frobenius Theorem.

Hokkaido Mathematical Journal, 55 (2026) pp.283-303

Fulltext

PDF

Abstract

The Perron-Frobenius theorem in infinite-dimensional Hilbert spaces can be breifly stated as follows: Given a Hilbert cone in a real Hilbert space, a bounded positive self-adjoint operator $A$ is ergodic with respect to this cone if and only if the maximum eigenvalue $\|A\|$ of $A$ is simple, and the corresponding eigenvector is strictly positive with respect to this cone. This paper addresses the inverse problem of the Perron-Frobenius theorem: Does there exist a Hilbert cone such that a given bounded positive self-adjoint operator $A$ becomes ergodic when its maximum eigenvalue $\|A\|$ is simple? We provide an affirmative answer to this question in this paper. Furthermore, we conduct a detailed analysis of a specialized Hilbert cone introduced to obtain this result. Additionally, we provide an illustrative example of an application of the obtained results to the heat semigroup generated by the magnetic Schrödinger operator.

Keywords	The Perron-Frobenius Theorem; Hilbert cones; Heat semigroups; Ergodicity;
msc2020(primary)	47D03; 20M99;

DE LIMA, Henrique F.; GOMES, Wallace F.; VELÁSQUEZ, Marco Antonio L.;

Codimension reduction of complete submanifolds in a class of weighted warped products.

Hokkaido Mathematical Journal, 55 (2026) pp.305-324

Fulltext

PDF

Abstract

In this paper, we deal with complete submanifolds immersed in a class of weighted warped products, focusing on codimension reduction results; more precisely, suitable geometric conditions which guarantee that these submanifolds are contained in slices of such an ambient space. For this, we assume suitable constraints on the Bakry-Émery-Ricci tensor and the weighted mean curvature vector field which enable us to apply several maximum principles. Applications to weighted minimal submanifolds in the Schwarzschild and Reissner-Nordström spaces with density are also given.

Keywords	Weighted warped product spaces; complete submanifolds; Bakry-Émery-Ricci tensor; $\varphi$-mean curvature vector field; $\varphi$-minimal submanifolds; codimension reduction results; Schwarzschild and Reissner-Nordström spaces;
msc2020(primary)	53C42; 53C40;