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Koji Fujiwara

Publications and source records attributed to Koji Fujiwara.

At least 19 recordsLinked to original sources
arXiv2026

Finite covers of a product of surfaces with bounded rank and arbitrarily large systole

We construct finite covers of a fixed product of two closed hyperbolic surfaces of genus two whose fundamental groups are generated by at most fifteen elements and whose injectivity radii tend to infinity. The construction uses fibre products over finite groups. These covers are closed aspherical four-manifolds with universal cover $\mathbb H^2\times\mathbb H^2$. They give counterexamples to a conjecture of Avramidi and Delzant for symmetric spaces of higher rank, in the case \(\mathbb H^2\times\mathbb H^2\).

math.GT↗
arXiv2026

Significant modulation of acoustoelectric current associated with charge density wave transitions

We studied acoustoelectric (AE) currents in materials that undergo charge density wave (CDW) transitions, induced by a surface acoustic wave (SAW) on a piezoelectric substrate. The polarity and magnitude of the AE current in NbSe$_3$ and 2H-TaSe$_2$ were modulated due to their CDW transitions. We also found that the sign of the AE current depends on the SAW propagation direction with respect to the crystalline axis of the substrate.A phenomenological model assuming strain-modified conductivity can qualitatively account for the significant modulation of the AE current associated with the CDW transition, as well as the SAW propagation orientation dependence. The present results offer a powerful probe for exploring SAW-electron interactions in van der Waals materials, thereby highlighting their potential for advancing the emerging field of straintronics.

cond-mat.mes-hall↗
arXiv2026

Small growth rates of free groups

We introduce the notion of a Magnus marking for a finite generating set of a group and prove a certain expansion property. Using this property, we determine the second and third smallest growth rates of the rank-$d$ free group for $d\ge 2$. We also give a new lower bound for the smallest growth rate of the genus-$g$ surface group for $g\ge 2$, as well as a lower bound for the growth rate associated with a one-relator presentation.

math.GR↗
arXiv2026

On K3 surfaces with hyperbolic automorphism groups

We show the finiteness of the Néron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic with explicit descriptions, under the assumption that the Picard number $\ge 6$ which is optimal to ensure the finiteness. Our proof of finiteness is based on the study of genus one fibrations on K3 surfaces and recent work of Kikuta and Takatsu.

math.AG↗
arXiv2025

Observation of Shapiro Steps in the Charge Density Wave State Induced by Strain on a Piezoelectric Substrate

Recent development in nanotechnology has enabled us to investigate the dynamic properties of van der Waals materials on a piezoelectric substrate. Here we report on the dynamics of charge density wave (CDW) in NbSe$_{3}$ nanowires induced by surface acoustic waves (SAWs). Clear peaks in the differential resistance were observed at the resonant frequency of the SAW device. These peaks known as Shapiro steps are typically observed by applying an rf current to NbSe$_{3}$ nanowires. We found that the Shapiro steps induced by SAWs show several distinct features from the ones induced by an rf current. Our detailed study revealed that a strain induced by SAWs plays a significant role in the Shapiro steps. The result clearly demonstrates the importance of the strain in CDW materials and paves the way for strain-induced device applications.

cond-mat.mes-hall↗
arXiv2025

Generation of a single-cycle surface acoustic wave pulse on LiNbO$_3$ for application to thin film materials

Surface acoustic wave (SAW) technology has been explored in thin-film materials to discover fundamental phenomena and to investigate their physical properties. It is used to excite and manipulate quasi-particles such as phonons or magnons, and can dynamically modulate the properties of the materials. In the field, SAWs are typically excited by a continuous wave at a resonant frequency. Recently, generation of a single-cycle SAW pulse has been demonstrated on GaAs substrate. Such a SAW pulse provides a potential to access a single quasi-particle excitation and to investigate its dynamics by time-resolved measurements. On the other hand, to modulate and control the properties of thin film materials, it is generally required to generate high-intensity SAWs. In this work, we demonstrate the efficient generation of a SAW pulse using a chirp interdigital transducer (IDT) on LiNbO$_3$ substrate. We have fabricated chirp IDT devices with bandwidths from 0.5 GHz to 5.5 GHz. We also confirmed the generation of a SAW pulse with 0.3 ns FWHM (full width at half maximum) by performing time-resolved measurements. The conversion efficiency between input power and SAW on LiNbO$_3$ substrate is approximately 45 times larger than that on GaAs substrate. This enables us to generate a high-intensity SAW pulse, meeting the requirement for the modulation of thin films. Our results will expand the research in the field, such as spintronics and magnonics, and lead to their further advancements.

cond-mat.mes-hall↗
arXiv2025

Hardy-Littlewood maximal operator on spaces of exponential volume growth

We consider the Hardy-Littlewood maximal function associated with ball averages on spaces with exponential volume growth. We focus on discrete groups with balls defined by invariant metrics associated with a variety of length functions. Under natural assumptions on the rough radial structure of the group in question, we establish a weak-type $\mathcal{L}\left(\log \mathcal{L}\right)^{\bf c}$ maximal inequality for the Hardy-Littlewood maximal function. We give a variety of examples where the rough radial structure assumptions hold, based on considerations from geometric group theory, or on analytic considerations related to the regular representation of the group. We elucidate the connections of these assumptions to a spherical coarse median inequality, to almost exact polynomial-exponential growth of balls, and to the radial rapid decay property. In particular, the weak-type maximal inequality in $\mathcal{L}\left(\log \mathcal{L}\right)^{\bf c}$ is established for any lattice in a connected semisimple Lie group with finite center, with respect to the distance function restricted from the Riemannian distance on symmetric space to an orbit of the lattice. It is also established for right-angled Artin groups, Coxeter groups and braid groups, for a suitable choice of word metric. For non-elementary word-hyperbolic group we establish that the Hardy-Littlewood maximal operator with respect to balls defined by a word length satisfies the weak-type $(1,1)$ maximal inequality, which is the optimal result.

math.DS↗
arXiv2023

The rates of growth in an acylindrically hyperbolic group

Let $G$ be an acylindrically hyperbolic group on a $δ$-hyperbolic space $X$. Assume there exists $M$ such that for any finite generating set $S$ of $G$, the set $S^M$ contains a hyperbolic element on $X$. Suppose that $G$ is equationally Noetherian. Then we show the set of the growth rates of $G$ is well-ordered (Theorem 1.1). The conclusion was known for hyperbolic groups, and this is a generalization. Our result applies to all lattices in simple Lie groups of rank-1 (Theorem 1.3), and more generally, some family of relatively hyperbolic groups (Theorem 1.2). It also applies to the fundamental group, of exponential growth, of a closed orientable $3$-manifold except for the case that the manifold has Sol-geometry (Theorem 5.7).

math.GR↗
arXiv2023

A coarse-geometry characterization of cacti

We give a quasi-isometric characterization of cacti, which is similar to Manning's characterization of quasi-trees by the bottleneck property. We also give another quasi-isometric characterization of cacti using fat theta curves.

math.MG↗
arXiv2023

The rates of growth in a hyperbolic group

We study the countable set of rates of growth of a hyperbolic group with respect to all its finite generating sets. We prove that the set is well-ordered, and that every real number can be the rate of growth of at most finitely many generating sets up to automorphism of the group. We prove that the ordinal of the set of rates of growth is at least $ω^ω$, and in case the group is a limit group (e.g., free and surface groups), it is $ω^ω$. We further study the rates of growth of all the finitely generated subgroups of a hyperbolic group with respect to all their finite generating sets. This set is proved to be well-ordered as well, and every real number can be the rate of growth of at most finitely many isomorphism classes of finite generating sets of subgroups of a given hyperbolic group. Finally, we strengthen our results to include rates of growth of all the finite generating sets of all the subsemigroups of a hyperbolic group.

math.GR↗
arXiv2021

Asymptotic dimension of planes and planar graphs

We show that the asymptotic dimension of a geodesic space that is homeomorphic to a subset in the plane is at most three. In particular, the asymptotic dimension of the plane and any planar graph is at most three.

math.MG↗
arXiv2021

The Farrell-Jones Conjecture for hyperbolic-by-cyclic groups

We prove the Farrell-Jones Conjecture for mapping tori of automorphisms of virtually torsion-free hyperbolic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture by Bartels-Lück-Reich, as well as the structure theory of mapping tori by Dahmani-Krishna.

math.GT↗
arXiv2020

Proper actions on finite products of quasi-trees

We say that a finitely generated group $G$ has property (QT) if it acts isometrically on a finite product of quasi-trees so that orbit maps are quasi-isometric embeddings. A quasi-tree is a connected graph with path metric quasi-isometric to a tree, and product spaces are equipped with the $\ell^1$-metric. As an application of the projection complex techniques, we prove that residually finite hyperbolic groups and mapping class groups have (QT).

math.GR↗
arXiv2019

Graph manifolds as ends of negatively curved Riemannian manifolds

Let $M$ be a graph manifold such that each piece of its JSJ decomposition has the $\Bbb H^2 \times \Bbb R$ geometry. Assume that the pieces are glued by isometries. Then, there exists a complete Riemannian metric on $\Bbb R \times M$ which is an "eventually warped cusp metric" with the sectional curvature $K$ satisfying $-1 \le K <0$. A theorem by Ontaneda then implies that $M$ appears as an end of a 4-dimensional, complete, non-compact Riemannian manifold of finite volume with sectional curvature $K$ satisfying $-1 \le K <0$.

math.DG↗
arXiv2018

Solvable groups of interval exchange transformations

We prove that any finitely generated torsion free solvable subgroup of the group ${\rm IET}$ of all Interval Exchange Transformations is virtually abelian. In contrast, the lamplighter groups $A\wr \mathbb{Z}^k$ embed in ${\rm IET}$ for every finite abelian group $A$, and we construct uncountably many non pairwise isomorphic 3-step solvable subgroups of ${\rm IET}$ as semi-direct products of a lamplighter group with an abelian group. We also prove that for every non-abelian finite group $F$, the group $F\wr \mathbb{Z}^k$ does not embed in ${\rm IET}$.

math.GR↗