Bulletin of the London Mathematical Society最新文献

We determine the differential Galois group of the family of all regular singular differential equations on the Riemann sphere. It is the free proalgebraic group on a set of cardinality $��\left|�C�\right|�$.

We show that in Euclidean 3-space any closed curve which contains the unit sphere within its convex hull has length $��L�⩾�4�\pi �$, and characterize the case of equality. This result generalizes the authors' recent solution to a conjecture of Zalgaller. Furthermore, for the analogous problem in $�n$ dimensions, we include the estimate $��L�⩾�C�n�\sqrt{�n�}�$ by Nazarov, which is sharp up to the constant $�C$.

We study the action of groups generated by bounded activity automata with infinite alphabets on their orbital Schreier graphs. We introduce an amenability criterion for such groups based on the recurrence of the first-level action. This criterion is a natural extension of the result that all groups generated by bounded activity automata with finite alphabets are amenable. Our motivation comes from the investigation of iterated monodromy groups of entire transcendental functions in holomorphic dynamics.

We prove the existence of finite groups acting freely as orientation-preserving homeomorphisms on closed orientable surfaces that extend as a group of homeomorphisms of some compact orientable 3-manifold but that cannot extend to a handlebody. This solves a basic problem in low-dimensional equivariant topology going back to the work of Reni and Zimmermann in the mid-1990s.

We consider families of conical Kähler–Einstein metrics on rank one horosymmetric Fano manifolds, with decreasing cone angles along a codimension one orbit. At the limit angle, which is positive, we show that the metrics, restricted to the complement of that orbit, converge to (the pull-back of) the Kähler–Einstein metric on the basis of the horosymmetric homogeneous space, which is a projective homogeneous space. Then we show that, on the symmetric space fibers, the rescaled metrics converge to Stenzel's Ricci flat Kähler metric.

The classical Liouville property says that all bounded harmonic functions in $�R^n$, that is, all bounded functions satisfying $��\Delta �f�=�0�$, are constant. In this paper, we obtain necessary and sufficient conditions on the symbol of a Fourier multiplier operator $��m�\left(�D�\right)�$, such that the solutions $�f$ to $��m�\left(�D�\right)�f�=�0�$ are Lebesgue a.e. constant (if $�f$ is bounded) or coincide Lebesgue a.e. with a polynomial (if $�f$ is polynomially bounded). The class of Fourier multipliers includes the (in general non-local) generators of Lévy processes. For generators of Lévy processes, we obtain necessary and sufficient conditions for a strong Liouville theorem where $�f$ is positive and grows at most exponentially fast. As an application of our results above, we prove a coupling result for space-time Lévy processes.

We prove that if, for a non-trivial variety of non-associative algebras, every subalgebra of every free algebra is free and $�I^2$ is an ideal whenever $�I$ is an ideal, then this variety coincides with the variety of all Lie algebras.

In this article, we address a problem posed by Bayart regarding the existence of an infinite-dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We fully resolve this problem by establishing the existence of the closed subspace. Furthermore, we prove that the set of supercyclic operators on $�{\ell }_1$ contains, up to the null operator, an isometric copy of $�{\ell }_1$.