Mostrando recursos 1 - 20 de 48

  1. Weighted Bott–Chern and Dolbeault cohomology for LCK-manifolds with potential

    ORNEA, Liviu; VERBITSKY, Misha; VULETESCU, Victor
    A locally conformally Kähler (LCK) manifold is a complex manifold, with a Kähler structure on its universal covering $\tilde M$, with the deck transform group acting on $\tilde M$ by holomorphic homotheties. One could think of an LCK manifold as of a complex manifold with a Kähler form taking values in a local system $L$, called the conformal weight bundle. The $L$-valued cohomology of $M$ is called Morse–Novikov cohomology; it was conjectured that (just as it happens for Kähler manifolds) the Morse–Novikov complex satisfies the $dd^c$-lemma, which (if true) would have far-reaching consequences for the geometry of LCK manifolds. In...

  2. A characterization of regular points by Ohsawa–Takegoshi extension theorem

    GUAN, Qi'an; LI, Zhenqian
    In this article, we present that the germ of a complex analytic set at the origin in $\mathbb{C}^n$ is regular if and only if the related Ohsawa–Takegoshi extension theorem holds. We also obtain a necessary condition of the $L^2$ extension of bounded holomorphic sections from singular analytic sets.

  3. Topology of mixed hypersurfaces of cyclic type

    INABA, Kazumasa; KAWASHIMA, Masayuki; OKA, Mutsuo
    Let $f_{II}({\boldsymbol{z}}, \bar{{\boldsymbol{z}}}) = z_{1}^{a_{1}+b_{1}}\bar{z}_{1}^{b_{1}}z_{2} + \cdots + z_{n-1}^{a_{n-1}+b_{n-1}}\bar{z}_{n-1}^{b_{n-1}}z_{n} + z_{n}^{a_{n}+b_{n}}\bar{z}_{n}^{b_{n}}z_{1}$ be a mixed weighted homogeneous polynomial of cyclic type and $g_{II}({\boldsymbol{z}}) = z_{1}^{a_{1}}z_{2} + \cdots + z_{n-1}^{a_{n-1}}z_{n} + z_{n}^{a_{n}}z_{1}$ be the associated weighted homogeneous polynomial where $a_{j} \geq 1$ and $b_{j} \geq 0$ for $j = 1, \dots, n$. We show that two links $S^{2n-1}_{\varepsilon} \cap f_{II}^{-1}(0)$ and $S^{2n-1}_{\varepsilon} \cap g_{II}^{-1}(0)$ are diffeomorphic and their Milnor fibrations are isomorphic.

  4. On the sequential polynomial type of modules

    GOTO, Shiro; NHAN, Le Thanh
    Let $M$ be a finitely generated module over a Noetherian local ring $R$. The sequential polynomial type $\mathrm{sp}(M)$ of $M$ was recently introduced by Nhan, Dung and Chau, which measures how far the module $M$ is from the class of sequentially Cohen–Macaulay modules. The present paper purposes to give a parametric characterization for $M$ to have $\mathrm{sp}(M)\le s$, where $s\ge -1$ is an integer. We also study the sequential polynomial type of certain specific rings and modules. As an application, we give an inequality between $\mathrm{sp}(S)$ and $\mathrm{sp}(S^G) $, where $S$ is a Noetherian local ring and $G$ is a...

  5. The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases

    GOMES, Diogo A.; MITAKE, Hiroyoshi; TRAN, Hung V.
    Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton–Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton–Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton–Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not directly apply. In this case, we establish the convergence by a direct approach.

  6. Basic relative invariants of homogeneous cones and their Laplace transforms

    NAKASHIMA, Hideto
    The purpose of this paper is to show that it is characteristic of symmetric cones among irreducible homogeneous cones that there exists a non-constant relatively invariant polynomial such that its Laplace transform is the reciprocal of a certain polynomial. To prove our theorem, we need the inductive structure of the basic relative invariants of a homogeneous cone. However, we actually work in a more general setting, and consider the inducing of the basic relative invariants from lower rank cones.

  7. Fermionic formula for double Kostka polynomials

    LIU, Shiyuan
    The $X=M$ conjecture asserts that the $1D$ sum and the fermionic formula coincide up to some constant power. In the case of type $A,$ both the $1D$ sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials $K_{{\boldsymbol\lambda},{\boldsymbol\mu}}(t),$ indexed by two double partitions ${\boldsymbol\lambda},{\boldsymbol\mu},$ are polynomials in $t$ introduced as a generalization of Kostka polynomials. In the present paper, we consider $K_{{\boldsymbol\lambda},{\boldsymbol\mu}}(t)$ in the special case where ${\boldsymbol\mu}=(-,\mu'')$. We formulate a $1D$ sum and a fermionic formula for $K_{{\boldsymbol\lambda},{\boldsymbol\mu}}(t),$ as a generalization of the case of ordinary Kostka polynomials. Then we prove an analogue of the...

  8. Time periodic problem for the compressible Navier–Stokes equation on $\mathbb{R}^2$ with antisymmetry

    TSUDA, Kazuyuki
    The compressible Navier–Stokes equation is considered on the two dimensional whole space when the external force is periodic in the time variable. The existence of a time periodic solution is proved for sufficiently small time periodic external force with antisymmetry condition. The proof is based on using the time-$T$-map associated with the linearized problem around the motionless state with constant density. In some weighted $L^\infty$ and Sobolev spaces the spectral properties of the time-$T$-map are investigated by a potential theoretic method and an energy method. The existence of a stationary solution to the stationary problem is also shown for sufficiently...

  9. A product formula for log Gromov–Witten invariants

    LEE, Yuan-Pin; QU, Feng
    The purpose of this short article is to prove a product formula relating the log Gromov–Witten invariants of $V \times W$ with those of $V$ and $W$ in the case the log structure on $V$ is trivial.

  10. Multiplicativity of the $\mathcal{I}$-invariant and topology of glued arrangements

    GUERVILLE-BALLÉ, Benoît
    The invariant $\mathcal{I}(\mathcal{A},\xi,\gamma)$ was first introduced by E. Artal, V. Florens and the author. Inspired by the idea of G. Rybnikov, we obtain a multiplicativity theorem of this invariant under the gluing of two arrangements along a triangle. An application of this theorem is to prove that the extended Rybnikov arrangements form an ordered Zariski pair (i.e. two arrangements with the same combinatorial information and different ordered topologies). Finally, we extend this method to a family of arrangements and thus we obtain a method to construct new examples of Zariski pairs.

  11. On Arakawa–Kaneko zeta-functions associated with $GL_2(\mathbb{C})$ and their functional relations

    KOMORI, Yasushi; TSUMURA, Hirofumi
    We construct a certain class of Arakawa–Kaneko zeta-functions associated with $GL_2(\mathbb{C})$, which includes the ordinary Arakawa–Kaneko zeta-function. We also define poly-Bernoulli polynomials associated with $GL_2(\mathbb{C})$ which appear in their special values of these zeta-functions. We prove some functional relations for these zeta-functions, which are regarded as interpolation formulas of various relations among poly-Bernoulli numbers. Considering their special values, we prove difference relations and duality relations for poly-Bernoulli polynomials associated with $GL_2(\mathbb{C})$.

  12. Analyticity of the Stokes semigroup in $BMO$-type spaces

    BOLKART, Martin; GIGA, Yoshikazu; SUZUKI, Takuya
    We consider the Stokes semigroup in a large class of domains including bounded domains, the half-space and exterior domains. We will prove that the Stokes semigroup is analytic in a certain type of solenoidal subspaces of $BMO$.

  13. A Hardy inequality and applications to reverse Hölder inequalities for weights on $\mathbb{R}$

    NIKOLIDAKIS, Eleftherios N.
    We prove a sharp integral inequality valid for non-negative functions defined on $[0,1]$, with given $L^1$ norm. This is in fact a generalization of the well known integral Hardy inequality. We prove it as a consequence of the respective weighted discrete analogue inequality whose proof is presented in this paper. As an application we find the exact best possible range of $p>q$ such that any non-increasing $g$ which satisfies a reverse Hölder inequality with exponent $q$ and constant $c$ upon the subintervals of $(0,1]$, should additionally satisfy a reverse Hölder inequality with exponent $p$ and in general a different constant...

  14. Laplace hyperfunctions in several variables

    HONDA, Naofumi; UMETA, Kohei
    We establish an edge of the wedge theorem for the sheaf of holomorphic functions with exponential growth at infinity and construct the sheaf of Laplace hyperfunctions in several variables. We also study the fundamental properties of the sheaf of Laplace hyperfunctions.

  15. Montesinos knots, Hopf plumbings, and L-space surgeries

    BAKER, Kenneth L.; MOORE, Allison H.
    Using Hirasawa–Murasugi's classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman–Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight contact structure on $S^3$. We also construct L-space knots with arbitrarily large tunnel number and discuss the question of whether L-space knots admit essential tangle decompositions in the context of satellite operations and tunnel number.

  16. On two-weight norm estimates for multilinear fractional maximal function

    SEHBA, Benoît Florent
    We prove some Sawyer-type characterizations for multilinear fractional maximal function for the upper triangle case. We also provide some two-weight norm estimates for this operator. As one of the main tools, we use an extension of the usual Carleson Embedding that is an analogue of the P. L. Duren extension of the Carleson Embedding for measures.

  17. Homogeneous affine surfaces: affine Killing vector fields and gradient Ricci solitons

    BROZOS-VÁZQUEZ, Miguel; GARCÍA-RÍO, Eduardo; GILKEY, Peter B.
    The homogeneous affine surfaces have been classified by Opozda. They may be grouped into 3 families, which are not disjoint. The connections which arise as the Levi-Civita connection of a surface with a metric of constant Gauss curvature form one family; there are, however, two other families. For a surface in one of these other two families, we examine the Lie algebra of affine Killing vector fields and we give a complete classification of the homogeneous affine gradient Ricci solitons. The rank of the Ricci tensor plays a central role in our analysis.

  18. Magidor cardinals

    GARTI, Shimon; HAYUT, Yair
    We define Magidor cardinals as Jónsson cardinals upon replacing colorings of finite subsets by colorings of $\aleph_0$-bounded subsets. Unlike Jónsson cardinals which appear at some low level of large cardinals, we prove the consistency of having quite large cardinals along with the fact that no Magidor cardinal exists.

  19. Foundation of symbol theory for analytic pseudodifferential operators, I

    AOKI, Takashi; HONDA, Naofumi; YAMAZAKI, Susumu
    A new symbol theory for pseudodifferential operators in the complex analytic category is given. Here the pseudodifferential operators mean integral operators with real holomorphic microfunction kernels. The notion of real holomorphic microfunctions had been introduced by Sato, Kawai and Kashiwara by using sheaf cohomology theory. Symbol theory for those operators was partly developed by Kataoka and by the first author and it has been effectively used in the analysis of operators of infinite order. However, there was a missing part that links the symbol theory and the cohomological definition of operators, that is, the consistency of the Leibniz–Hörmander rule and...

  20. Foundation of symbol theory for analytic pseudodifferential operators, I

    AOKI, Takashi; HONDA, Naofumi; YAMAZAKI, Susumu
    A new symbol theory for pseudodifferential operators in the complex analytic category is given. Here the pseudodifferential operators mean integral operators with real holomorphic microfunction kernels. The notion of real holomorphic microfunctions had been introduced by Sato, Kawai and Kashiwara by using sheaf cohomology theory. Symbol theory for those operators was partly developed by Kataoka and by the first author and it has been effectively used in the analysis of operators of infinite order. However, there was a missing part that links the symbol theory and the cohomological definition of operators, that is, the consistency of the Leibniz–Hörmander rule and...

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