Mostrando recursos 1 - 20 de 65

  1. $\delta$-homogeneity in Finsler geometry and the positive curvature problem

    Xu, Ming; Zhang*, Lei
    In this paper, we explore the similarity between normal homogeneity and $\delta$-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected $\delta$-homogeneous Finsler space is $G$-$\delta$-homogeneous, for some suitably chosen connected quasi-compact $G$. So $\delta$-homogeneous Finsler metrics can be defined by a bi-invariant singular metric on $G$ and submersion, just as normal homogeneous metrics, using a bi-invariant Finsler metric on $G$ instead. More careful analysis shows, in the space of all Finsler metrics on $G/H$, the subset of all $G$-$\delta$-homogeneous ones is in fact the closure for the subset of all $G$-normal ones, in...

  2. A rigidity of equivariant holomorphic maps into a complex Grassmannian induced from orthogonal direct sums of holomorphic line bundles

    Koga, Isami
    In the present paper, we study holomorphic maps induced from orthogonal direct sums of holomorphic line bundles over a compact simply connected homogeneous Kähler manifold into a complex Grassmannian. Then we show if such maps are equivariant, then they are unique up to complex isometry.

  3. Asymptotic behavior of the solutions for the Laplace equation with a large spectral parameter and the inhomogeneous Robin type conditions

    Ikehata*, Masaru; Kawashita**, Mishio
    Reduced problems are elliptic problems with a large parameter (as the spectral parameter) given by the Laplace transform of time dependent problems. In this paper, asymptotic behavior of the solutions of the reduced problem for the classical heat equation in bounded domains with the inhomogeneous Robin type conditions is discussed. The boundary of the domain consists of two disjoint surfaces, outside one and inside one. When there are inhomogeneous Robin type data at both boundaries, it is shown that asymptotics of the value of the solution with respect to the large parameter at a given point inside the domain is...

  4. Representations of quantized coordinate algebras via PBW-type elements

    Oya, Hironori
    Inspired by the work of Kuniba-Okado-Yamada, we study some tensor product representations of quantized coordinate algebras of symmetrizable Kac-Moody Lie algebras in terms of quantized enveloping algebras. As a consequence, we describe structures and properties of certain reducible representations of quantized coordinate algebras. This paper includes alternative proofs of Soibelman's tensor product theorem and Kuniba-Okado-Yamada's common structure theorem based on our direct calculation method using global bases.

  5. Global existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth and superlinear production

    Nakaguchi, Etsushi; Osaki, Koichi
    We study the global existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth. We introduce superlinear production of a chemoattractant. We then show the global existence of solutions in $L_p$ space $( p > n )$ under certain relations between the degradation and production orders.

  6. On five dimensional Sasakian Lie algebras with trivial center

    Loiudice, E.; Lotta, A.
    We show that every five-dimensional Sasakian Lie algebra with trivial center is $\varphi$-symmetric. Moreover starting from a particular Sasakian structure on the Lie group $SL(2,\mathbb{R})\times\text{Aff}(\mathbb{R})$ we obtain a family of contact metric $(k,\mu)$ structures whose Boeckx invariants assume all values less than $-1$.

  7. The arc metric on Teichmüller spaces of surfaces of infinite type with boundary

    Chen, Qiyu; Liu, Lixin
    Let $X_{0}$ be a complete hyperbolic surface of infinite type with geodesic boundary which admits a countable pair of pants decomposition. As an application of the Basmajian identity for complete bordered hyperbolic surfaces of infinite type with limit sets of 1-dimensional measure zero, we define an asymmetric metric (which is called arc metric) on the quasiconformal Teichmüller space $\mathcal{T}(X_{0})$ provided that $X_{0}$ satisfies a geometric condition. Furthermore, we construct several examples of hyperbolic surfaces of infinite type satisfying the geometric condition and discuss the relation between the Shiga's condition and the geometric condition.

  8. Groups of automorphisms of bordered orientable Klein surfaces of topological genus 2

    Bujalance, E.; Etayo, J.J.; Martínez, E.
    In this paper, we obtain the groups of automorphisms of orientable bordered Klein surfaces of topological genus $2$. For each of those groups $G$ we determine the values of $k$ such that $G$ acts on a surface with $k$ boundary components. Besides, for each given $k$ we exhibit the groups acting on a surface with $k$ boundary components.

  9. Groups of automorphisms of bordered orientable Klein surfaces of topological genus 2

    Bujalance, E.; Etayo, J.J.; Martínez, E.
    In this paper, we obtain the groups of automorphisms of orientable bordered Klein surfaces of topological genus $2$. For each of those groups $G$ we determine the values of $k$ such that $G$ acts on a surface with $k$ boundary components. Besides, for each given $k$ we exhibit the groups acting on a surface with $k$ boundary components.

  10. Groups of automorphisms of bordered orientable Klein surfaces of topological genus 2

    Bujalance, E.; Etayo, J.J.; Martínez, E.
    In this paper, we obtain the groups of automorphisms of orientable bordered Klein surfaces of topological genus $2$. For each of those groups $G$ we determine the values of $k$ such that $G$ acts on a surface with $k$ boundary components. Besides, for each given $k$ we exhibit the groups acting on a surface with $k$ boundary components.

  11. Groups of automorphisms of bordered orientable Klein surfaces of topological genus 2

    Bujalance, E.; Etayo, J.J.; Martínez, E.
    In this paper, we obtain the groups of automorphisms of orientable bordered Klein surfaces of topological genus $2$. For each of those groups $G$ we determine the values of $k$ such that $G$ acts on a surface with $k$ boundary components. Besides, for each given $k$ we exhibit the groups acting on a surface with $k$ boundary components.

  12. Realizing homology classes up to cobordism

    Grant, Mark; SZŰCS, András; Terpai, Tamás
    It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod $2$ homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient.

  13. Realizing homology classes up to cobordism

    Grant, Mark; SZŰCS, András; Terpai, Tamás
    It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod $2$ homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient.

  14. Realizing homology classes up to cobordism

    Grant, Mark; SZŰCS, András; Terpai, Tamás
    It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod $2$ homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient.

  15. Realizing homology classes up to cobordism

    Grant, Mark; SZŰCS, András; Terpai, Tamás
    It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod $2$ homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient.

  16. Perturbation of irregular Weyl-Heisenberg wave packet frames in $L^2(\mathbb{R})$

    Kumar, Raj; SAH, Ashok K.
    In this paper, we consider the perturbation problem of irregular Weyl-Heisenberg wave packet frame $\{D_{a_j}T_{bk}E_{c_m}\psi\}_{j,k,m\in \mathbb{Z}}$ about dilation, translation and modulation parameters. We give a method to determine whether the perturbation systems is a frame for wave packet functions whose Fourier transforms have small support and prove the stability about dilation parameter on Paley-Wiener space. For a wave packet function, we give a definite answer to the stability about translation parameter $b$.

  17. Perturbation of irregular Weyl-Heisenberg wave packet frames in $L^2(\mathbb{R})$

    Kumar, Raj; SAH, Ashok K.
    In this paper, we consider the perturbation problem of irregular Weyl-Heisenberg wave packet frame $\{D_{a_j}T_{bk}E_{c_m}\psi\}_{j,k,m\in \mathbb{Z}}$ about dilation, translation and modulation parameters. We give a method to determine whether the perturbation systems is a frame for wave packet functions whose Fourier transforms have small support and prove the stability about dilation parameter on Paley-Wiener space. For a wave packet function, we give a definite answer to the stability about translation parameter $b$.

  18. Perturbation of irregular Weyl-Heisenberg wave packet frames in $L^2(\mathbb{R})$

    Kumar, Raj; SAH, Ashok K.
    In this paper, we consider the perturbation problem of irregular Weyl-Heisenberg wave packet frame $\{D_{a_j}T_{bk}E_{c_m}\psi\}_{j,k,m\in \mathbb{Z}}$ about dilation, translation and modulation parameters. We give a method to determine whether the perturbation systems is a frame for wave packet functions whose Fourier transforms have small support and prove the stability about dilation parameter on Paley-Wiener space. For a wave packet function, we give a definite answer to the stability about translation parameter $b$.

  19. Perturbation of irregular Weyl-Heisenberg wave packet frames in $L^2(\mathbb{R})$

    Kumar, Raj; SAH, Ashok K.
    In this paper, we consider the perturbation problem of irregular Weyl-Heisenberg wave packet frame $\{D_{a_j}T_{bk}E_{c_m}\psi\}_{j,k,m\in \mathbb{Z}}$ about dilation, translation and modulation parameters. We give a method to determine whether the perturbation systems is a frame for wave packet functions whose Fourier transforms have small support and prove the stability about dilation parameter on Paley-Wiener space. For a wave packet function, we give a definite answer to the stability about translation parameter $b$.

  20. On ramified torsion points on a curve with stable reduction over an absolutely unramified base

    Hoshi, Yuichiro
    Let $p$ be an odd prime number, $W$ an {\it absolutely unramified} $p$-adically complete discrete valuation ring with algebraically closed residue field, and $X$ a curve of genus at least two over the field of fractions $K$ of $W$. In the present paper, we study, under the assumption that $X$ has {\it stable reduction} over $W$, {\it torsion points} on $X$, i.e., torsion points of the Jacobian variety $J$ of $X$ which lie on the image of the Albanese embedding $X\hookrightarrow J$ with respect to a $K$-rational point of $X$. A consequence of the main result of the present paper...

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