Bulletin of the London Mathematical Society最新文献

We study the conformal classes of two-dimensional Lorentzian tori with (nonzero) Killing fields. We define a map that associate to such a class a vector field on the circle (up to a scalar factor). This map is not injective but has finite-dimensional fiber. It allows us to characterize the conformal classes of tori with Killing field satisfying a condition related to the existence of conjugate points given by Mehidi.

We prove that at differentiability points $��r_0�>�0�$ of the volume function of a compact set $��A�\subset �R^d�$ (associating to $�r$ the volume of the $�r$-parallel set of $�A$), the surface area measures of $�r$-parallel sets of $�A$ converge weakly to the surface area measure of the $�r_0$-parallel set as $��r�\to �r_0�$. We further study the question which sets of parallel radii can occur as sets of nondifferentiability points of the volume function of some compact set. We provide a full characterization for dimensions $��d�=�1�$ and 2.

Dominic Welsh was born in Port Talbot on 29 August 1938, the eldest child in a family of educators, and died in Oxford on 30 November 2023. He was the first student from his school to attend the University of Oxford, where he remained for the rest of his life as a Fellow of Merton College and a Professor of the University. He combined excellence as tutor and supervisor over nearly 40 years with a distinguished research record in probability and discrete mathematics, where he excelled in both original and expository work. With his DPhil supervisor John Hammersley, he introduced first-passage percolation, and in so doing formulated and proved the first subadditive ergodic theorem. His is the ‘W’ in the ‘RSW’ method that is now central to the theory of random planar media. He was a pioneer in matroid theory with numerous significant results and conjectures, and his monograph has been influential. He worked on computational complexity and particularly the complexity of computing the Tutte polynomial. Throughout his career, he inspired generations of undergraduates and postgraduates, and through his personal enthusiasm and warmth he helped develop a community of scholars in aspects of combinatorics who remember him with love and respect.

This note has two related but independent parts. Firstly, we prove a generalisation of a recent result of Gay on the smooth mapping class group of $�S^4$. Secondly, we give an alternative proof of a consequence of work of Saeki, namely that the Dehn twist along the boundary sphere of a simply connected closed smooth 4-manifold $�X$ with $��\partial �X�\cong �S^3�$ is trivial after taking connected sums with enough copies of $��S^2�\times �S^2�$.

We consider the classical problem of determining the largest possible cardinality of a minimal presentation of a numerical monoid with given embedding dimension and multiplicity. Very few values of this cardinality are known. In addressing this problem, we apply tools from Hilbert functions and free resolutions of artinian standard graded algebras. This approach allows us to solve the problem in many cases and, at the same time, identify subtle difficulties in the remaining cases. As a by-product of our analysis, we deduce results for the corresponding problem for the type of a numerical monoid.

In this paper, we study sharp maximal function estimates for multilinear pseudo-differential operators. Our target is operators of type (0,0) for which a differentiation does not make any decay of the associated symbol. Analogous results for operators of type $��(�\rho �,�\rho �)�$, , appeared in an earlier work of the authors [17], but a different approach is given for $��\rho �=�0�$.