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

We show that, given $��k�⩾�3�$, there exist $�k$-player quantum XOR games for which the entangled bias can be arbitrarily larger than the bias of the game when the players are restricted to separable strategies. In particular, quantum entanglement can be a much more powerful resource than local operations and classical communication to play these games. This result shows a strong contrast to the bipartite case, where it was recently proved that, as a consequence of a noncommutative version of Grothendieck theorem, the entangled bias is always upper bounded by a universal constant times the one-way classical communication bias. In this sense, our main result can be understood as a counterexample to an extension of such a noncommutative Grothendieck theorem to multilinear forms.

We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in $�R^2$. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a uniqueness result.

For a log Calabi Yau pair ($��X�,�D�$) with $��X�\setminus �D�$ smooth affine, satisfying either a maximal degeneracy assumption or contains a Zariski dense torus, we prove under the condition that D is the support of a nef divisor that the structure constants defining a trace form on the mirror algebra constructed by Gross–Siebert are given by the naive curve counts defined by Keel–Yu. As a corollary, we deduce that the equality of the mirror algebras constructed by Gross–Siebert and Keel–Yu in the case $��X�\setminus �D�$ contains a Zariski dense torus. In addition, we use this result to prove a mirror conjecture proposed by Mandel for Fano pairs satisfying the maximal degeneracy assumption.

In this article, we prove that for a definable set in an o-minimal structure with connected link (at 0 or infinity), the inner distance of the link is equivalent to the inner distance of the set restricted to the link. With this result, we obtain several consequences. We present also several relations between the local and the global Lipschitz geometry of singularities. For instance, we prove that two sets in Euclidean spaces, not necessarily definable in an o-minimal structure, are outer lipeomorphic if and only if their stereographic modifications are outer lipeomorphic if and only if their inversions are outer lipeomorphic.

For large classes of even-dimensional Riemannian manifolds $��(�M�,�g�)�$, we construct and analyze conformally invariant random fields. These centered Gaussian fields $��h�=�h_g�$, called co-polyharmonic Gaussian fields, are characterized by their covariance kernels k which exhibit a precise logarithmic divergence: $��|�k��(�x�,�y�)��-�\log �\frac{1}{�d�(�x�,�y�)�}�|�\le �C�$. They share a fundamental quasi-invariance property under conformal transformations. In terms of the co-polyharmonic Gaussian field $�h$, we define the Liouville Quantum Gravity measure, a random measure on $�M$, heuristically given as

In this paper, we study the hyperbolic and parabolic strip deformations of ideal (possibly once-punctured) hyperbolic polygons whose vertices are decorated with horoballs. We prove that the interiors of their arc complexes parametrise the open convex set of all uniformly lengthening infinitesimal deformations of the decorated hyperbolic metrics on these surfaces, motivated by the work of Danciger–Guéritaud–Kassel. We also give a version of this result for the undecorated ideal polygons and once-punctured ideal polygons.