Journal of the London Mathematical Society-Second Series最新文献

In this paper, we are interested in characterizing the standard contact sphere in terms of dynamically convex contact manifolds, which admit a Liouville filling with vanishing symplectic homology. We first observe that if the filling is flexible, then those contact manifolds are contactomorphic to the standard contact sphere. We then investigate quantitative geometry of those contact manifolds focusing on similarities with the standard contact sphere in filtered symplectic homology.

We complete the classification of automorphism groups of del Pezzo surfaces over algebraically closed fields of odd positive characteristic.

In this paper, we present some new results on the geometrically $�m$-step solvable Grothendieck conjecture in anabelian geometry. Specifically, we show the (weak bianabelian and strong bianabelian) geometrically $�m$-step solvable Grothendieck conjecture(s) for affine hyperbolic curves over fields finitely generated over the prime field. First of all, we show the conjecture over finite fields. Next, we show the geometrically $�m$-step solvable version of the Oda–Tamagawa good reduction criterion for hyperbolic curves. Finally, by using these two results, we show the conjecture over fields finitely generated over the prime field.

We show that the Lipschitz-free space with the Radon–Nikodým property and a Daugavet point recently constructed by Veeorg is in fact a dual space isomorphic to $�{\ell }_1$. Furthermore, we answer an open problem from the literature by showing that there exists a superreflexive space, in the form of a renorming of $�{\ell }_2$, with a $�\Delta$-point. Building on these two results, we are able to renorm every infinite-dimensional Banach space to have a $�\Delta$-point. Next, we establish powerful relations between existence of $�\Delta$-points in Banach spaces and their duals. As an application, we obtain sharp results about the influence of $�\Delta$-points for the asymptotic geometry of Banach spaces. In addition, we prove that if $�X$ is a Banach space with a shrinking $�k$-unconditional basis with $��k�<�2�$, or if $�X$ is a Hahn–Banach smooth space with a dual satisfying the Kadets–Klee property, then $�X$ and its dual $�{}^{}$

We find all $�K$-polystable smooth Fano threefolds that can be obtained as blowup of $�P^3$ along the disjoint union of a twisted cubic curve and a line.

We show that any compact nonpositively curved cube complex $�Y$ embeds in a compact nonpositively curved cube complex $�R$ where each combinatorial injective partial local isometry of $�Y$ extends to an automorphism of $�R$. When $�Y$ is special and the collection of injective partial local isometries satisfies certain conditions, we show that $�R$ can be chosen to be special and the embedding $��Y�\hookrightarrow �R�$ can be chosen to be a local isometry.

Let $�G$ be a linear algebraic group, not necessarily connected or reductive, over the field of real numbers $�R$. We describe a method, implemented on computer, to find the first Galois cohomology set $��H^1��(�R�,�G�)��$. The output is a list of 1-cocycles in $�G$. Moreover, we describe an implemented algorithm that, given a 1-cocycle $��z�\in �Z^1��(�R�,�G�)��$, finds the cocycle in the computed list to which $�z$ is equivalent, together with an element of $��G�\left(�C�\right)�$ realizing the equivalence.

We extend the Duffin–Schaeffer conjecture to the setting of systems of $�m$ linear forms in $�n$ variables. That is, we establish a criterion to determine whether, for a given rate of approximation, almost all or almost no $�n$-by-$�m$ systems of linear forms are approximable at that rate using integer vectors satisfying a natural coprimality condition. When $��m�=�n�=�1�$, this is the classical 1941 Duffin–Schaeffer conjecture, which was proved in 2020 by Koukoulopoulos and Maynard. Pollington and Vaughan proved the higher dimensional version, where $��m�>�1�$ and $��n�=�1�$, in 1990. The general statement we prove here was conjectured in 2009 by Beresnevich, Bernik, Dodson, and Velani. For approximations with no coprimality requirement, they also conjectured a generalized version of Catlin's conjecture, and in 2010, Beresnevich and Velani proved the $��m�>�1�$ cases of that. Catlin's classical conjecture, where $��m�=�n�=�1�$, follows from the classical Duffin–Schaeffer conjecture. The remaining cases of the generalized version, where

For each non-flat, unimodular Ricci soliton solvmanifold $��(�S_0�,�g_0�)�$, we construct a one-parameter family of complete, expanding, gradient Ricci solitons that admit a cohomogeneity one isometric action by $�S_0$. The orbits of this action are hypersurfaces homothetic to $��(�S_0�,�g_0�)�$. These metrics are asymptotic at one end to an Einstein solvmanifold. In the one-parameter family, exactly one metric is Einstein, and exactly one has orbits that are isometric to $��(�S_0�,�g_0�)�$.

In 1992, Hsiao and Liu first showed that the solution to the compressible Euler equations with damping time-asymptotically converges to the diffusion wave $��(�\overline{v}�,�\overline{u}�)�$ of the porous media equation. Geng et al. proposed a time-asymptotic expansion around the diffusion wave $��(�\overline{v}�,�\overline{u}�)�$, which is a better asymptotic profile than $��(�\overline{v}�,�\overline{u}�)�$. In this paper, we rigorously justify the time-asymptotic expansion by the approximate Green function method and the energy estimates. Moreover, the large time behavior of the solution to compressible Euler equations with damping is accurately characterized by the time-asymptotic expansion.