Bulletin of the London Mathematical Society最新文献

A method of solving nonlinear boundary value problems involving $��(�p�,�q�)�$-Laplace with unbounded measurable coefficients is introduced through the inverse optimal problem approach. The existence, uniqueness, and stability of the nonnegative weak solution to the nonlinear equations of the form

We show that a dynamical sequence $�{�\left(�f_n�\right)�}_{�n�\in �N�}$ of polynomials over a number field whose set of stable primes is of positive density must necessarily have a very restricted, and, in particular, virtually prosolvable dynamical Galois group. Together with existing heuristics, our results suggest, moreover, that a polynomial $�f$ all of whose iterates are irreducible modulo a positive density subset of the primes must necessarily be a composition of linear functions, monomials, and Dickson polynomials.

We prove a variant of the theorem of Ito–Michler, investigating the properties of finite groups where a prime number $�p$ does not divide the degree of any irreducible character left invariant by some Galois automorphism of order $�p$.

The fundamental group of the complement of a locally flat surface in a 4-manifold is called the knot group of the surface. In this article, we prove that two locally flat 2-spheres in $��C�P^2�$ with knot group $�Z_2$ are ambiently isotopic if they are homologous. This combines with work of Tristram and Lee–Wilczyński, as well as the classification of $�Z$-surfaces, to complete a proof of the statement: a class $��d�\in �H_2��\left(�C�P^2�\right)��\cong �Z�$ is represented by a locally flat sphere with abelian knot group if and only if $��\left|�d�\right|�\in �\{�0�,�1�,�2�\}�$; and this sphere is unique up to ambient isotopy.

Let $�S$ be a closed surface of genus at least 2, let $�h$ be a smooth metric of curvature on $�S$, and let $�h_0$ be a hyperbolic metric on $�S$. We show that there exists a unique quasifuchsian AdS spacetime with left metric isotopic to $�h_0$, containing a past-convex Cauchy surface with induced metric isotopic to $�h$.

Let $�X$ be a real analytic manifold endowed with a distance satisfying suitable properties and let $�k$ be a field. In [Petit and Schapira, Selecta Math. 29 (2023), no. 70, DOI 10.1007/s00029-023-00875-6], the authors construct a pseudo-distance on the derived category of sheaves of $�k$-modules on $�X$, generalizing a previous construction of [Kashiwara and Schapira, J. Appl. Comput. Math. Topol. 2 (2018), 83–113]. We prove here that if the distance between two constructible sheaves with compact support (or more generally, constructible sheaves up to infinity) on $�X$ is zero, then these two sheaves are isomorphic, answering a question of [Kashiwara and Schapira, J. Appl. Comput. Math. Topol. 2 (2018), 83–113]. We also prove that our results imply a similar statement for finitely presentable persistence modules due to Lesnick.

In this paper, we give a Burns–Krantz rigidity result on some fibered domains. As an application, we obtain the Burns–Krantz rigidity on bounded symmetric domains.

We disprove the generalized Chern–Hamilton conjecture on the existence of critical compatible metrics on contact 3-manifolds. More precisely, we show that a contact 3-manifold $��(�M�,�\alpha �)�$ admits a critical compatible metric for the Chern–Hamilton energy functional if and only if it is Sasakian or its associated Reeb flow is $�C^{\infty }$-conjugate to an algebraic Anosov flow modeled on $��\stackrel{\sim }{�S�L�}��(�2�,�R�)��$. In particular, this yields a complete topological classification of compact 3-manifolds that admit critical compatible metrics. As a corollary, we prove that no contact structure on $�T^3$ admits a critical compatible metric and that critical compatible metrics can only occur when the contact structure is tight.

In this work, we prove that many Apéry-like sequences arising from modular forms satisfy the Lucas congruences modulo any prime. As an implication, we completely affirm four conjectural Lucas congruences that were recently posed by S. Cooper and reinterpret a number of known results.

In [Algebraic surfaces and hyperbolic geometry, Cambridge University Press, Cambridge, 2012], Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur in Section 7 of [Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 14–50]. We give examples of rational surfaces with the same property. Our examples $�Y$ are Looijenga pairs, that is, there is a connected singular nodal curve $��D�\subset �Y�$ such that $��K_Y�+�D�=�0�$.