Bulletin of the London Mathematical Society最新文献

In this paper, inspired by Brendle (Comm. Pure Appl. Math. 76 (2023), 2192) and Johne (arXiv:2103.08496, 2021), we prove a Sobolev inequality on manifolds with density and asymptotically nonnegative Bakry–Émery Ricci curvature.

In this paper, we prove that the hyperfocal subalgebra of a block with an abelian defect group and a cyclic hyperfocal subgroup is Rickard equivalent to the group algebra of the semidirect of the hyperfocal subgroup by the inertial quotient of the block. In particular, the hyperfocal subalgebra is a Brauer tree algebra, which is analogous to the structure of blocks with cyclic defect groups. As a consequence, we show that Broué's abelian defect group conjecture holds for blocks with cyclic hyperfocal subgroups.

Assuming Lehmer's conjecture, we estimate the degree of the trace field $��K�\left(�M_{�p�/�q�}�\right)�$ of a hyperbolic Dehn filling $�M_{�p�/�q�}$ of a 1-cusped hyperbolic 3-manifold $�M$ by

In this paper, we study a multiplier operator which is induced by the Schwarzian derivative of univalent functions with a quasiconformal extension to the extended complex plane. As applications, we show that the Brennan conjecture is satisfied for a large class of quasidisks. We also establish a new characterization of asymptotically conformal curves and of the Weil–Petersson curves in terms of the multiplier operator.

We study the normalized volume of toric singularities. As it turns out, there is a close relation to the notion of (nonsymmetric) Mahler volume from convex geometry. This observation allows us to use standard tools from convex geometry, such as the Blaschke–Santaló inequality and Radon's theorem to prove nontrivial facts about the normalized volume in the toric setting. For example, we prove that for every $��\epsilon �>�0�$ there are only finitely many $�Q$-Gorenstein toric singularities with normalized volume at least $�\epsilon$. From this result it directly follows that there are also only finitely many toric Sasaki–Einstein manifolds of volume at least $�\epsilon$ in each dimension. Additionally, we show that the normalized volume of every toric singularity is bounded from above by that of the rational double point of the same dimension. Finally, we discuss certain bounds of the normalized volume in terms of topological invariants of resolutions of the singularity. We establish two upper bounds in terms of the Euler characteristic and of the first Chern class, respectively. We show that a lower bound, which was conjectured earlier by He, Seong, and Yau, is closely related to the nonsymmetric Mahler conjecture in convex geometry.

We extend Loeper's $�L^2$-estimate (Theorem 2.9 in J. Math. Pures Appl. (9) 86 (2006), no. 1, 68–79) relating the force fields to the densities for the Vlasov–Poisson system to $�L^p$, with $��1�<�p�<�+�\infty �$, based on the Helmholtz–Weyl decomposition. This allows us to generalize both the classical Loeper's 2-Wasserstein stability estimate (Theorem 1.2 in J. Math. Pures Appl. (9) 86 (2006), no. 1, 68–79) and the recent stability estimate by the first author relying on the newly introduced kinetic Wasserstein distance (Theorem 3.1 in Arch Rational Mech. Anal. 244 (2022), no. 1, 27–50) to kinetic Wasserstein distances of order $��1�<�p�<�+�\infty �$.

In this paper, we prove Selberg's announced result on $�r$-gaps between zeros of the Riemann zeta-function $�\zeta$. Our proof uses a result on variations of $��arg�\zeta �$ by Tsang based on Selberg's method. The same result with explicit constants under the Riemann Hypothesis has been obtained by Conrey and Turnage-Butterbaugh using a different method. We explain how to obtain explicit constants under the Riemann Hypothesis using our approach which is based on Selberg's and Tsang's arguments.

A group $�G$ is invariably generated if there exists a subset $��S�\subseteq �G�$ such that, for every choice $��g_s�\in �G�$ for $��s�\in �S�$, the group $�G$ is generated by $��\{�s^{g_s}�\mid �s�\in �S�\}�$. Gelander, Golan, and Juschenko (J. Algebra 478 (2016), 261–270) showed that Thompson groups $�T$ and $�V$ are not invariably generated. Here, we generalize this result to the larger setting of rearrangement groups, proving that any subgroup of a rearrangement group that has a certain transitive property is not invariably generated.