Proceedings of the American Mathematical Society最新文献

We prove that minimizers of the L d L^{d} -norm of the Hessian in the unit ball of R d mathbb {R}^d are locally of class C 1 , α C^{1,alpha } . Our findings extend previous results on Hessian-dependent functionals to the borderline case and resonate with the Hölder regularity theory available for elliptic equations in double-divergence form.

We consider word complexity and topological entropy for random substitution subshifts. In contrast to previous work, we do not assume that the underlying random substitution is compatible. We show that the subshift of a primitive random substitution has zero topological entropy if and only if it can be obtained as the subshift of a deterministic substitution, answering in the affirmative an open question of Rust and Spindeler [Indag. Math. (N.S.) 29 (2018), pp. 1131–1155]. For constant length primitive random substitutions, we develop a systematic approach to calculating the topological entropy of the associated subshift. Further, we prove lower and upper bounds that hold even without primitivity. For subshifts of non-primitive random substitutions, we show that the complexity function can exhibit features not possible in the deterministic or primitive random setting, such as intermediate growth, and provide a partial classification of the permissible complexity functions for subshifts of constant length random substitutions.

In this note, we relate the basepoint-freeness threshold of a polarized abelian variety, introduced by Jiang and Pareschi, with k k -jet very ampleness. Then, we derive several applications of this fact, including a criterion for the k k -very ampleness of Kummer varieties.

Consider a symmetric space G / H G/H with simple Lie group G G . We demonstrate that when G / H G/H is not irreducible, it is necessarily even dimensional and noncompact. Furthermore, the subgroup H H is also both noncompact and non-semisimple. Additionally, we establish that the only G G -invariant connection on G / H G/H is the canonical connection. On the other hand, we show that if G / H G/H has an odd dimension, it must be irreducible, and the subgroup H H must be semisimple. Finally, we present an explicit example,

In this note, we provide an adaptation of the Kohler-Jobin rearrangement technique to the setting of the Gauss space. As a result, we prove the Gaussian analogue of the Kohler-Jobin resolution of a conjecture of Pólya-Szegö: when the Gaussian torsional rigidity of a domain is fixed, the Gaussian principal frequency is minimized for the half-space. At the core of this rearrangement technique is the idea of considering a “modified” torsional rigidity, with respect to a given function, and rearranging its layers to half-spaces, in a particular way; the Rayleigh quotient decreases with this procedure.

We emphasize that the analogy of the Gaussian case with the Lebesgue case is not to be expected here, as in addition to some soft symmetrization ideas, the argument relies on the properties of some special functions; the fact that this analogy does hold is somewhat of a miracle.

We consider the problem of estimating the eigenvalues and the integral of the corresponding eigenfunctions, associated to the Newtonian potential operator, defined in a bounded domain Ω ⊂ R d Omega subset mathbb {R}^{d} , where d = 2 , 3 d=2,3 , in terms of the maximum radius of Ω Omega . We first provide these estimations in the particular case of a ball and a disc. Then we extend them to general shapes using a, derived, monotonicity property of the eigenvalues of the Newtonian operator. The derivation of the lower bounds is quite tedious for the 2D-Logarithmic potential operator. Such upper/lower bounds appear naturally while estimating the electric/acoustic fields propagating in R d mathbb {R}^{d} in the presence of small scaled and highly heterogeneous particles.

We provide necessary and sufficient conditions for operator-valued functions on arbitrary sets associated with a collection of test functions to have factorizations in several situations.

We prove that a virtually periodic object in an abelian category gives rise to a non-vanishing result on certain Hom groups in the singularity category. Consequently, for any artin algebra with infinite global dimension, its singularity category has no silting subcategory, and the associated differential graded Leavitt algebra has a non-vanishing cohomology in each degree. We verify the Singular Presilting Conjecture for singularly-minimal algebras and ultimately-closed algebras. We obtain a trichotomy on the Hom-finiteness of the cohomologies of differential graded Leavitt algebras.

Let p ≥ 7 p geq 7 be a prime number. Let S ( 3 ) S(3) denote the third Morava stabilizer algebra. In recent years, Kato-Shimomura and Gu-Wang-Wu found several families of nontrivial products in the stable homotopy ring of spheres π ∗ ( S ) pi _* (S) using H ∗ , ∗ ( S ( 3 ) ) H^{*,*} (S(3)) . In this paper, we determine all nontrivial products in π ∗ ( S ) pi _* (S) of the Greek letter family elements