Bulletin of the London Mathematical Society最新文献

Given a polynomial $�p$ with no zeros in the polydisk, or equivalently the poly-upper half-plane, we study the problem of determining the ideal of polynomials $�q$ with the property that the rational function $��q�/�p�$ is bounded near a boundary zero of $�p$. We give a complete description of this ideal of numerators in the case where the zero set of $�p$ is smooth and satisfies a nondegeneracy condition. We also give a description of the ideal in terms of an integral closure when $�p$ has an isolated zero on the distinguished boundary. Constructions of multivariate stable polynomials are presented to illustrate sharpness of our results and necessity of our assumptions.

We prove that for any second-countable, locally compact group $�G$, any continuous $�G$-action on the primitive ideal space of a separable, nuclear $�C^{*}$-algebra $�B$ such that $��B�\cong �B�\otimes �O_2�\otimes �K�$ is induced by an action on $�B$. As a direct consequence, we establish that every continuous action on the primitive ideal space of a separable, nuclear $�C^{*}$-algebra is induced by an action on a $�C^{*}$-algebra with the same primitive ideal space. Moreover, we discuss an application to the classification of equivariantly $�O_2$-stable actions.

We show that, given a closed integral symplectic manifold $��(�\Sigma �,�\omega �)�$ of dimension $��2�n�⩾�4�$, for every integer $��k�>�{\int }_{\Sigma }�{\omega }^n�$, the Boothby–Wang bundle over $��(�\Sigma �,�k�\omega �)�$ carries no Stein fillable contact structure. This negatively answers a question raised by Eliashberg. A similar result holds for Boothby–Wang orbibundles. As an application, we prove the non-smoothability of some isolated singularities.

Relying substantially on work of Garg, Gurvits, Oliveira and Wigderson, it is shown that geometric Brascamp–Lieb data are, in a certain sense, dense in the space of feasible Brascamp–Lieb data. This addresses a question raised by Bennett and Tao in their recent work on the adjoint Brascamp–Lieb inequality.

In this paper, we consider the following Lane–Emden system:

We describe a mistake in Corollary 3.2 as well as a mistake in Lemma 3.4 of Reber [Bull. London Math. Soc. 55 (2023), no. 6, 3077–3096], and give an alternative proof of the main result.

This work addresses the question of density of piecewise constant (resp. rigid) functions in the space of vector-valued functions with bounded variation (resp. deformation) with respect to the strict convergence. Such an approximation property cannot hold when considering the usual total variation in the space of measures associated to the standard Frobenius norm in the space of matrices. It turns out that oscillation and concentration phenomena interact in such a way that the Frobenius norm has to be homogenized into a (resp. symmetric) Schatten-1 norm that coincides with the Euclidean norm on rank-one (resp. symmetric) matrices. By means of explicit constructions consisting of the superposition of sequential laminates, the validity of an optimal approximation property is established at the expense of endowing the space of measures with a total variation associated with the homogenized norm in the space of matrices.

We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local–nonlocal operator $��L�=�-�\Delta �+�{�(�-�\Delta �)�}^s�$, with a power-like source term. We show that the so-called Fujita phenomenon holds, and the critical value is exactly the same as for the fractional Laplacian.

Let $�G$ be a residually finite, good group of finite virtual cohomological dimension. We prove that the natural monomorphism $��G�\hookrightarrow �\hat{G}�$ induces a bijective correspondence between conjugacy classes of finite $�p$-subgroups of $�G$ and those of its profinite completion $�\hat{G}$. Moreover, we prove that the centralizers and normalizers in $�\hat{G}$ of finite $�p$-subgroups of $�G$ are the closures of the respective centralizers and normalizers in $�G$. With somewhat more restrictive hypotheses, we prove the same results for finite solvable subgroups of $�G$. In the last section, we give a few applications of this theorem to hyperelliptic mapping class groups and virtually compact special toral relatively hyperbolic groups (these include fundamental groups of 3-orbifolds and of uniform standard arithmetic hyperbolic orbifolds).