Mostrando recursos 1 - 20 de 2.286

  1. Extrinsic circular trajectories on totally η-umbilic real hypersurfaces in a complex hyperbolic space

    Bao, Tuya; Adachi, Toshiaki
    A trajectory for a Sasakian magnetic field, which is a generalization of geodesics, on a real hypersurface in a complex hyperbolic space CHn is said to be extrinsic circular if it can be regarded as a circle as a curve in CHn. We study how the moduli space of extrinsic circular trajectories, which is the set of their congruence classes, on a totally η-umbilic real hypersurface is contained in the moduli space of circles in CHn. From this aspect we characterize tubes around totally geodesic complex hypersurfaces CHn-1 in CHn by some properties of such trajectories.

  2. Sublinear tracking in Thurston's metric for random walks

    Pan, Huiping
    In this paper, we prove the sublinear tracking property in Thurston's metric for sample paths of random walks on mapping class group.

  3. Curved folding and planar cutting of simple closed curve on a conical origami

    Choi, Ikhan
    The fold-and-cut theorem states that one can find a flat folding of paper, so that one complete straight cut on the folding creates any desired polygon. We extend this problem to curved origami for piecewise C1 simple closed curves. Many of those curves on paper turn out to be cut by a straight plane after we fold the paper into a conical shape—the surface consists of half-lines with a common vertex. Let γ: I → R2 be a piecewise C1 simple closed curve such that there exists a parametrization γ(ψ)= (r(ψ) cos ψ, r(ψ) sin ψ) on ψ $\in$ [0,2π)...

  4. On p-biharmonic submanifolds in nonpositively curved manifolds

    Cao, Xiangzhi; Luo, Yong
    Let u: (M, g) → (N, h) be a map between Riemannian manifolds (M, g) and (N, h). The p-bienergy of u is τp(u) = ∫M|τ(u)|pg, where τ(u) is the tension field of u and p > 1. Critical points of τp are called p-biharmonic maps and isometric p-biharmonic maps are called p-biharmonic submanifolds. When p = 2, p-biharmonic submanifolds are biharmonic submanifolds and in recent years many nonexistence results are found for biharmonic submanifolds in nonpositively curved manifolds. In this paper we will study the nonexistence result for general p-biharmonic submanifolds.

  5. Hypersurfaces in Euclidean spaces with finite total curvature

    Zhu, Peng
    We discuss complete noncompact hypersurfaces in the Euclidean space Rn+1 with finite total curvature. We obtain vanishing result and finiteness theorem for the space of L2 harmonic 2-forms. These results are generalized versions of results for L2 harmonic 1-forms.

  6. Well-posedness and decay property for the generalized damped Boussinesq equation with double rotational inertia

    Zhang, Zaiyun; Huang, Jianhua; Sun, Mingbao
    In this paper, we investigate the initial value problem (IVP henceforth) associated with the generalized damped Boussinesq equation with double rotational inertia ¶ $$\left\{\begin{array}{ll} u_{tt}+\gamma\Delta^2 u_{tt}-a\Delta u_{tt}-2b\Delta u_t-\alpha\Delta^3u+\beta\Delta^2 u-\Delta u=\Delta f(u),\quad x \in\mathbb{R}^n, \; t<0, \\ u(x,0)=u_0(x),\quad u_t(x,0)=u_1(x),\quad x \in\mathbb{R}^n. \end{array}\right.$$ ¶ Based on decay estimates of solutions to the corresponding linear equation, we establish the decay estimates and the pointwise estimates by using Fourier transform. Under small condition on the initial data, we obtain the existence and asymptotic behavior of global solutions in the corresponding Sobolev spaces by time weighted norms technique and the contraction mapping principle.

  7. Subgroups of the Torelli group generated by two symmetric bounding pair maps

    Stukow, Michał
    Let {a,b} and {c,d} be two pairs of bounding simple closed curves on an oriented surface which intersect nontrivialy. We prove that if these pairs are invariant under the action of an orientation reversing involution, then the corresponding bounding pair maps generate a free group. This supports the conjecture stated by C. Leininger and D. Margalit that any pair of elements of the Torelli group either commute or generate a free group.

  8. On the isometries from the unit disk to infinite dimensional Teichmüller spaces

    Ohtake, Hiromi
    We generalize Earle-Li's polydisk theorem and embedding theorem, and study isometries from the unit disk to infinite dimensional Teichmüller spaces. We also give a simple proof that for any non-Strebel point τ, there exist infinitely many real analytic geodesic disks through τ and the basepoint in infinitely dimensional Teichmüller spaces.

  9. On a certain family of asymmetric Riemann surfaces with the cyclic automorphism group

    Kozłowska-Walania, Ewa; Tyszkowska, Ewa
    A compact Riemann surface X of genus g ≥ 2 is called asymmetric or pseudo-real if it admits an anticonformal automorphism but no anticonformal involution. The order d = #(δ) of an anticonformal automorphism δ of such a surface is divisible by 4. In the particular case where d = 4, δ is a pseudo-symmetry and the surface is called pseudo-symmetric. ¶ A Riemann surface X is said to be p-hyperelliptic if it admits a conformal involution ρ for which the orbit space X/<ρ> has genus p. This notion is the particular case of so called cyclic (q,n)-gonal surface which...

  10. Notes on the value distribution of ff(k)-b

    Lü, Weiran; Liu, Nana; Yang, Chungchun; Zhuo, Caiping
    Let f denote a transcendental meromorphic function with N(r, f) = S(r, f) and k be an integer. By using methods different from others, we have been able to derive several new results and pose some new conjectures that relate to the yet to be resolved conjecture concerning the quantitative estimates on the zeros of ff(k)-b, for a non-vanishing small function b.

  11. Rigidity of closed metric measure spaces with nonnegative curvature

    Wu, Jia-Yong
    We show that one-dimensional circle is the only case for closed smooth metric measure spaces with nonnegative Bakry-Émery Ricci curvature whose spectrum of the weighted Laplacian has an optimal positive upper bound. This result extends the work of Hang-Wang in the manifold case (Int. Math. Res. Not. 18 (2007), Art. ID rnm064, 9pp).

  12. A formula for the algebraic degree in semidefinite programming

    Hiep, Dang Tuan
    In this paper we use the Bott residue formula in equivariant cohomology to show a formula for the algebraic degree in semidefinite programming.

  13. Ricci tensors on three-dimensional almost coKähler manifolds

    Wang, Yaning
    Let M3 be a three-dimensional almost coKähler manifold such that the Ricci curvature of the Reeb vector field is invariant along the Reeb vector field. In this paper, we obtain some classification results of M3 for which the Ricci tensor is η-parallel or the Riemannian curvature tensor is harmonic.

  14. On combinatorial criteria for non-degenerate singularities

    Brzostowski, Szymon; Oleksik, Grzegorz
    In this article we give a sufficient and necessary condition for a Kouchnirenko non-degenerate holomorphic function to have an isolated singularity at 0 in terms of its support. As a corollary we give some useful sufficient conditions for singularity to be isolated.

  15. Balls in quaternionic hyperbolic manifolds

    Cao, Wensheng
    By use of the Zassenhaus neighborhood of Sp(n,1), we obtain an explicit lower bound for the radius of the largest inscribed ball in quaternionic hyperbolic n-manifold $\mathcal{M}$ = HHn/Γ. As an application, we obtain a lower bound for the volumes of quaternionic hyperbolic n-manifolds.

  16. A sharp smoothness of the conjugation of class P-homeomorphisms to diffeomorphisms

    Adouani, Abdelhamid; Marzougui, Habib
    Let f be a class P-homeomorphism of the circle. We prove that there exists a piecewise analytic homeomorphism that conjugate f to a one-class P with prescribed break points lying on pairwise distinct orbits. As a consequence, we give a sharp estimate for the smoothness of a conjugation of class P-homeomorphism f of the circle satisfying the (D)-property (i.e. the product of f-jumps in the break points contained in a same orbit is trivial), to diffeomorphism. When f does not satisfy the (D)-property the conjugating homeomorphism is never a class P and even more it is not absolutely continuous function...

  17. Douady-Earle extension of the strongly symmetric homeomorphism

    Wu, Yan; Qi, Yi
    It is shown that the complex dilatation of the Douady-Earle extension of a strongly symmetric homeomorphism induces a vanishing Carleson measure on the unit disk D. As application, it is proved that the VMO-Teichmüller space is a subgroup of the universal Teichmüller space.

  18. Tikhonov regularization for Dunkl multiplier operators

    Soltani, Fethi
    We study some class of Dunkl multiplier operators Tk,m; and we give for them an application of the theory of reproducing kernels to the Tikhonov regularization, which gives the best approximation of the operators Tk,m on the Dunkl-type Paley-Wiener spaces Hh.

  19. On convexity of simple closed frontals

    Fukunaga, Tomonori; Takahashi, Masatomo
    We study convexity of simple closed frontals of Legendre curves in the Euclidean plane by using the curvature of Legendre curves. We show that for a Legendre curve, the simple closed frontal under conditions is convex if and only if the sign of both functions of the curvature of the Legendre curve does not change. We also give some examples of convex simple closed frontals.

  20. A construction of lattices in splittable solvable Lie groups

    Yamada, Takumi
    In this paper, we consider a unified constructions of lattices in splittable solvable Lie groups.

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