Mostrando recursos 1 - 20 de 28

  1. Classification results of quasi Einstein solitons

    Huang, Shu Yau; Wang, Lin Feng
    We classify (ρ,τ)-quasi Einstein solitons with (a,τ)-concurrent vector fields. We also give a necessary and sufficient condition for a submanifold to be a (ρ,τ)-quasi Einstein soliton in a Riemannian manifold equipped with an (a,τ)-concurrent vector field.

  2. Classification results of quasi Einstein solitons

    Huang, Shu Yau; Wang, Lin Feng
    We classify (ρ,τ)-quasi Einstein solitons with (a,τ)-concurrent vector fields. We also give a necessary and sufficient condition for a submanifold to be a (ρ,τ)-quasi Einstein soliton in a Riemannian manifold equipped with an (a,τ)-concurrent vector field.

  3. The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one

    Hoshi, Yuichiro; Kinoshita, Ryo; Nakayama, Chikara
    We study the Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one. A consequence of the main results is that the isomorphism class of a certain moduli space of hyperbolic curves of genus one over a sub-p-adic field is completely determined by the isomorphism class of the étale fundamental group of the moduli space over the absolute Galois group of the sub-p-adic field. We also prove related results in absolute anabelian geometry.

  4. The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one

    Hoshi, Yuichiro; Kinoshita, Ryo; Nakayama, Chikara
    We study the Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one. A consequence of the main results is that the isomorphism class of a certain moduli space of hyperbolic curves of genus one over a sub-p-adic field is completely determined by the isomorphism class of the étale fundamental group of the moduli space over the absolute Galois group of the sub-p-adic field. We also prove related results in absolute anabelian geometry.

  5. On endomorphisms of hypersurfaces

    Karzhemanov, Ilya
    For any prime p ≥ 5, we show that generic hypersurface Xp $subset$ Pp defined over Q admits a non-trivial rational dominant self-map of degree > 1, defined over $\overline{\mathbb{Q}}$ . A simple arithmetic application of this fact is also given.

  6. On endomorphisms of hypersurfaces

    Karzhemanov, Ilya
    For any prime $p \geq 5$, we show that generic hypersurface $X_{p} \subset \mathbf{P}^{p}$ defined over $\mathbf{Q}$ admits a non-trivial rational dominant self-map of degree $> 1$, defined over ${\mathbf{\bar {Q}}}$. A simple arithmetic application of this fact is also given.

  7. Absolute zeta functions and the automorphy

    Kurokawa, Nobushige; Tanaka, Hidekazu

  8. Absolute zeta functions and the automorphy

    Kurokawa, Nobushige; Tanaka, Hidekazu

  9. A note on Atiyah's Γ-index theorem in Heisenberg calculus

    Seto, Tatsuki
    In this note, we prove an index theorem on Galois coverings for Heisenberg elliptic (but not elliptic) differential operators, which is analogous to Atiyah's Γ-index theorem. This note also contains an example of Heisenberg differential operators with non-trivial Γ-index.

  10. A note on Atiyah's Γ-index theorem in Heisenberg calculus

    Seto, Tatsuki
    In this note, we prove an index theorem on Galois coverings for Heisenberg elliptic (but not elliptic) differential operators, which is analogous to Atiyah's Γ-index theorem. This note also contains an example of Heisenberg differential operators with non-trivial Γ-index.

  11. Ground state solutions for asymptotically periodic linearly coupled Schrödinger equations with critical exponent

    Chen, Sitong; Tang, XianHua; Li, Jianxiong
    We consider the following system of coupled nonlinear Schrödinger equations ¶ $$\left\{\begin{array}{ll}-\triangle u+a(x) u=|u|^{p-2}u+\lambda(x) v, x\in \mathbb{R}^N,\\-\triangle v+b(x) v=|v|^{2^*-2}v+\lambda(x) u, x\in \mathbb{R}^N,\\u,v\in H^1(\mathbb{R}^N), \end{array}\right.$$ ¶ where N ≥ 3, 2 < p < 2*, 2* = 2N/(N−2) is the Sobolev critical exponent, a, b, λ $\in$ C(RN, R) $\cap$ L(RN, R) and a(x), b(x) and λ(x) are asymptotically periodic, and can be sign-changing. By using a new technique, we prove the existence of a ground state of Nehari type solution for the above system under some mild assumptions on a, b and λ. In particular, the common condition that |λ(x)| < $\sqrt{a(x)b(x)}$ for...

  12. Ground state solutions for asymptotically periodic linearly coupled Schrödinger equations with critical exponent

    Chen, Sitong; Tang, XianHua; Li, Jianxiong
    We consider the following system of coupled nonlinear Schrödinger equations $$\left\{ \begin{array}\\-\Delta u + a(x)u = \vert u \vert^{p-2}u + \lambda(x)v, \quad x \in \mathbf{R}^{N},\\ -\Delta v + b(x)v = \vert v \vert^{2^{*}-2}v + \lambda(x)u, \quad x \in \mathbf{R}^{N},\\ u, v \in H^{1} (\mathbf{R}^{N}), \end{array} \right.$$ where $N \geq 3, 2 \lt p \lt 2^{*}, 2^{*} = 2N / (N - 2)$ is the Sobolev critical exponent, $a, b, \lambda \in C(\mathbf{R}^{N}, \mathbf{R}) \cap L^{\infty} (\mathbf{R}^{N}, \mathbf{R})$ and $a(x)$, $b(x)$ and $\lambda(x)$ are asymptotically periodic, and can be sign-changing. By using a new technique, we prove the existence of a...

  13. On infinitesimal Strebel points

    Fletcher, Alastair
    In this paper, we prove that if X is a Riemann surface of infinite analytic type and [μ]T is any element of Teichmüller space, then there exists μ1 $\in$ [μ]T so that [μ1]B is an infinitesimal Strebel point.

  14. On infinitesimal Strebel points

    Fletcher, Alastair
    In this paper, we prove that if $X$ is a Riemann surface of infinite analytic type and $[\mu]_T$ is any element of Teichmüller space, then there exists $\mu _{1} \in [\mu]_{T}$ so that $[\mu_1]_{B}$ is an infinitesimal Strebel point.

  15. Note on restriction maps of Chow rings to Weyl group invariants

    Yagita, Nobuaki
    Let G be an algebraic group over C corresponding a compact simply connected Lie group. When H*(G) has p-torsion, we see ρ*CH: CH*(BG) → CH*(BT)WG(T) is always not surjective. We also study the algebraic cobordism version ρ*Ω. In particular when G = Spin(7) and p = 2, we see each Griffiths element in CH*(BG) is detected by an element in Ω*(BT).

  16. Note on restriction maps of Chow rings to Weyl group invariants

    Yagita, Nobuaki
    Let G be an algebraic group over C corresponding a compact simply connected Lie group. When H*(G) has p-torsion, we see ρ*CH: CH*(BG) → CH*(BT)WG(T) is always not surjective. We also study the algebraic cobordism version ρ*Ω. In particular when G = Spin(7) and p = 2, we see each Griffiths element in CH*(BG) is detected by an element in Ω*(BT).

  17. L p p-harmonic 1-forms on locally conformally flat Riemannian manifolds

    Han, Yingbo; Zhang, Qianyu; Liang, Mingheng
    In this paper, we obtain some vanishing and finiteness theorems for Lp p-harmonic 1-forms on a locally conformally flat Riemmannian manifolds which satisfies an integral pinching condition on the traceless Ricci tensor, and for which the scalar curvature satisfies pinching curvature conditions or the first eigenvalue of the Laplace-Beltrami operator of M is bounded by a suitable constant.

  18. L p p-harmonic 1-forms on locally conformally flat Riemannian manifolds

    Han, Yingbo; Zhang, Qianyu; Liang, Mingheng
    In this paper, we obtain some vanishing and finiteness theorems for Lp p-harmonic 1-forms on a locally conformally flat Riemmannian manifolds which satisfies an integral pinching condition on the traceless Ricci tensor, and for which the scalar curvature satisfies pinching curvature conditions or the first eigenvalue of the Laplace-Beltrami operator of M is bounded by a suitable constant.

  19. Almost automorphic solutions of semilinear stochastic hyperbolic differential equations in intermediate space

    Xia, Zhinan
    In this paper, we investigate the existence, uniqueness of almost automorphic in one-dimensional distribution mild solution for semilinear stochastic differential equations driven by Lévy noise. The semigroup theory, fixed point theorem and stochastic analysis technique are the main tools in carrying out proof. Finally, we give one example to illustrate the main findings.

  20. Almost automorphic solutions of semilinear stochastic hyperbolic differential equations in intermediate space

    Xia, Zhinan
    In this paper, we investigate the existence, uniqueness of almost automorphic in one-dimensional distribution mild solution for semilinear stochastic differential equations driven by Lévy noise. The semigroup theory, fixed point theorem and stochastic analysis technique are the main tools in carrying out proof. Finally, we give one example to illustrate the main findings.

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