Mathematische Annalen最新文献

We study holomorphic maps F from a smooth Levi non-degenerate real hypersurface $M_{\ell }\subset C^n$ into a hyperquadric $H_{{\ell }^{\text{'}}}^N$ with signatures $\ell \le (n-1)/2$ and ${\ell }^{\text{'}}\le (N-1)/2,$ respectively. Assuming that $N-n<n-1,$ we prove that if $\ell ={\ell }^{\text{'}},$ then F is either CR transversal to $H_{\ell }^N$ at every point of $M_{\ell },$ or it maps a neighborhood of $M_{\ell }$ in $C^n$ into $H_{\ell }^N.$ Furthermore, in the case where ${\ell }^{\text{'}}>\ell ,$ we show that if F is not CR transversal at $0\in M_{\ell },$ then it must be transversally flat. The latter is best possible.

We present an adjunction formula for foliations on varieties and we consider applications of the adjunction formula to the cone theorem for rank one foliations and the study of foliation singularities.

Assuming a modular version of Schanuel's conjecture and the modular Zilber-Pink conjecture, we show that the existence of generic solutions of certain families of equations involving the modular j function can be reduced to the problem of finding a Zariski dense set of solutions. By imposing some conditions on the field of definition of the variety, we are also able to obtain versions of this result without relying on these conjectures, and even a result including the derivatives of j.

We develop a theory of quasisymmetries for finitely ramified fractals, with applications to finitely ramified Julia sets. We prove that certain finitely ramified fractals admit a naturally defined class of "undistorted metrics" that are all quasisymmetrically equivalent. As a result, piecewise-defined homeomorphisms of such a fractal that locally preserve the cell structure are quasisymmetries. This immediately gives a solution to the quasisymmetric uniformization problem for topologically rigid fractals such as the Sierpiński triangle. We show that our theory applies to many finitely ramified Julia sets, and we prove that any connected Julia set for a hyperbolic unicritical polynomial has infinitely many quasisymmetries, generalizing a result of Lyubich and Merenkov. We also prove that the quasisymmetry group of the Julia set for the rational function [Formula: see text] is infinite, and we show that the quasisymmetry groups for the Julia sets of a broad class of polynomials contain Thompson's group F.

We give a new short proof of the theorem due to Marquis and Sabok, which states that the orbit equivalence relation induced by the action of a finitely generated hyperbolic group on its Gromov boundary is hyperfinite. Our methods permit moreover to show that every such action has finite Borel asymptotic dimension.

We use twisted relative Picard varieties to split Brauer classes on projective varieties over algebraically closed fields by torsors for a fixed abelian scheme independent of the Brauer class. The construction is also used to prove that the index of an unramified Brauer class divides a fixed power of its period.

We introduce two families of generators (functions) $G$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results are proved on the density of separated sets that provide non-uniform sampling for the shift-invariant and quasi shift-invariant spaces generated by elements of these families. As an application, new sharp results are obtained on the density of semi-regular lattices for the Gabor frames generated by elements from these families.

We generalize results from topological robotics on the topological complexity (TC) of aspherical spaces to sectional categories of fibrations inducing subgroup inclusions on the level of fundamental groups. In doing so, we establish new lower bounds on sequential TCs of aspherical spaces as well as the parametrized TC of epimorphisms. Moreover, we generalize the Costa-Farber canonical class for TC to classes for sequential TCs and explore their properties. We combine them with the results on sequential TCs of aspherical spaces to obtain results on spaces that are not necessarily aspherical.

We give a new proof of the boundedness of bilinear Schur multipliers of second order divided difference functions, as obtained earlier by Potapov, Skripka and Sukochev in their proof of Koplienko's conjecture on the existence of higher order spectral shift functions. Our proof is based on recent methods involving bilinear transference and the Hörmander-Mikhlin-Schur multiplier theorem. Our approach provides a significant sharpening of the known asymptotic bounds of bilinear Schur multipliers of second order divided difference functions. Furthermore, we give a new lower bound of these bilinear Schur multipliers, giving again a fundamental improvement on the best known bounds obtained by Coine, Le Merdy, Potapov, Sukochev and Tomskova. More precisely, we prove that for $f\in C^2\left(R\right)$ and $1<p,p_1,p_2<\infty$ with $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}$ we have $\begin{array}{c}\Vert M_{f^{\left[2\right]}}:S_{p_1}\times S_{p_2}\to S_p\Vert \lesssim \Vert f^{\text{'}\text{'}}{\Vert }_{\infty }D(p,p_1,p_2),\end{array}$ where the constant $D(p,p_1,p_2)$ is specified in Theorem 7.1 and $D(p,2p,2p)\approx p^4{p}^{\ast }$ with $p^{\ast }$ the Hölder conjugate of p. We further show that for $f\left(\lambda \right)=\lambda \left|\lambda \right|,$ $\lambda \in R,$ for every $1<p<\infty$ we have