Mathematische Zeitschrift最新文献

On the twisted Fock spaces ( {mathcal {F}}^lambda ({{mathbb {C}}}^{2n}) ) we consider two types of convolution operators ( S_varphi ^lambda ) and ( {widetilde{S}}_varphi ^lambda ) associated to an element ( varphi in {mathcal {F}}^lambda ({{mathbb {C}}}^{2n}).) We find a necessary and sufficient condition on ( varphi ) so that ( S_varphi ^lambda ) (resp. ( {widetilde{S}}_varphi ^lambda ) ) is bounded on ( {mathcal {F}}^lambda ({{mathbb {C}}}^{2n}).) We show that for any given non constant ( varphi ) at least one of these two operators is unbounded.

We construct automorphisms of ({{mathbb {C}}}^2) of constant Jacobian with a cycle of escaping Fatou components, on which there are exactly two limit functions, both of rank 1. On each such Fatou component, the limit sets for these limit functions are two disjoint hyperbolic subsets of the line at infinity. In the literature there are currently very few examples of automorphisms of ({{mathbb {C}}}^2) with rank one limit sets on the boundary of Fatou components. To our knowledge, this is the first example in which such limit sets are hyperbolic, and moreover different limit sets of rank 1 coexist.

In this paper we exhibit for every non amenable group that is initially sub-amenable (sometimes also referred to as LEA), two sofic approximations that are not conjugate by any automorphism of the universal sofic group. This addresses a question of Pǎunescu and generalizes the Elek–Szabo uniqueness theorem for sofic approximations.

Fix a positive integer N and a real number (0< beta < 1/(N+1)). Let (Gamma ) be the homogeneous symmetric Cantor set generated by the IFS

For (min mathbb {Z}_+) we show that there exist infinitely many translation vectors ({textbf{t}}=(t_0,t_1,ldots , t_m)) with (0=t_0<t_1<cdots <t_m) such that the union (bigcup _{j=0}^m(Gamma +t_j)) is a self-similar set. Furthermore, for (0< beta < 1/(2N+1)), we give a finite algorithm to determine whether the union (bigcup _{j=0}^m(Gamma +t_j)) is a self-similar set for any given vector ({textbf{t}}). Our characterization relies on determining whether some related directed graph has no cycles, or whether some related adjacency matrix is nilpotent.

We compute the one-level density of the non-trivial zeros of the Riemann zeta-function weighted by (|zeta (frac{1}{2}+it)|^{2k}) for (k=1) and, for test functions with Fourier support in ((-frac{1}{2},frac{1}{2})), for (k=2). As a consequence, for (k=1,2), we deduce under the Riemann hypothesis that (T(log T)^{1-k^2+o(1)}) non-trivial zeros of (zeta ), of imaginary parts up to T, are such that (zeta ) attains a value of size ((log T)^{k+o(1)}) at a point which is within (O(1/log T)) from the zero.

We give a new proof for the interior regularity of strictly convex solutions of the Monge–Ampère equation. Our approach uses a doubling inequality for the Hessian in terms of the extrinsic distance function on the maximal Lagrangian submanifold determined by the potential equation.

Given a calibration (alpha ) whose stabilizer acts transitively on the Grassmanian of calibrated planes, we introduce a nontrivial Lie-theoretic condition on (alpha ), which we call compliancy, and show that this condition holds for many interesting geometric calibrations, including Kähler, special Lagrangian, associative, coassociative, and Cayley. We determine a sufficient condition that ensures compliancy of (alpha ), we completely characterize compliancy in terms of properties of a natural involution determined by a calibrated plane, and we relate compliancy to the geometry of the calibrated Grassmanian. The condition that a Riemannian immersion (iota :L rightarrow M) be calibrated is a first order condition. By contrast, its extrinsic geometry, given by the second fundamental form A and the induced tangent and normal connections (nabla ) on TL and D on NL, respectively, is second order information. We characterize the conditions imposed on the extrinsic geometric data ((A, nabla , D)) when the Riemannian immersion (iota :L rightarrow M) is calibrated with respect to a calibration (alpha ) on M which is both parallel and compliant. This motivate the definition of an infinitesimally calibrated Riemannian immersion, generalizing the classical notion of a superminimal surface in ({mathbb {R}}^4).

In this paper, we confirm the Fino–Vezzoni Conjecture for unimodular Lie algebras which contain abelian ideals of codimension two, a natural generalization to the class of almost abelian Lie algebras. This provides new evidence towards the validity of the conjecture on a very special type of 3-step solvmanifolds.

We prove the existence of a gap around zero for canonical height functions associated with endomorphisms of projective spaces defined over complex function fields. We also prove that if the rational points of height zero are Zariski dense, then the endomorphism is birationally isotrivial. As a corollary, by a result of S. Cantat and J. Xie, we have a geometric Northcott property on projective plane in the same spirit of results of R. Benedetto, M. Baker and L. Demarco on the projective line.

We prove the existence of a unique smooth solution to the quaternionic Monge–Ampère equation for ((n-1))-quaternionic plurisubharmonic (psh) functions on a compact hyperKähler manifold and thus obtain solutions to the quaternionic form-type equation. We derive the (C^0) estimate by establishing a Cherrier-type inequality as in Tosatti and Weinkove (J Am Math Soc 30(2):311–346, 2017). By adopting the approach of Dinew and Sroka (Geom Funct Anal 33(4):875–911, 2023) to our context, we obtain the (C^1) and (C^2) estimates without assuming the flatness of underlying hyperKähler metric comparing to the previous result Gentili and Zhang (J Geom Anal 32:9, 2022).