American Journal of Mathematics最新文献

abstract:

We consider the problem of prescribing the $sigma_k$-curvature on the standard sphere $Bbb{S}^n$ with $ngeq 3$. We prove existence and compactness theorems when $kgeq n/2$. This extends an earlier result of Chang, Han, and Yang for $n=4$ and $k=2$.

abstract:

Let $F$ be a non-archimedean local field of residue characteristic $pneq 2$. Let $G$ be a connected reductive group over $F$ that splits over a tamely ramified extension of $F$. In~2001, Yu constructed types which are called {it tame supercuspidal types} and conjectured that Hecke algebras associated with these types are isomorphic to Hecke algebras associated with depth-zero types of some twisted Levi subgroups of $G$. In this paper, we prove this conjecture. We also prove that the Hecke algebra associated with a {it regular supercuspidal type} is isomorphic to the group algebra of a certain abelian group.

abstract:

We prove the density hypothesis for wide families of arithmetic orbifolds arising from all division quaternion algebras over all number fields of bounded degree. Our power-saving bounds on the multiplicities of non-tempered representations are uniform in the volume and spectral aspects.

abstract:

The current work considers solutions to the wave equation on asymptotically flat, stationary, Lorentzian spacetimes in $(1+3)$ dimensions. We investigate the relationship between the rate at which the geometry tends to flat and the pointwise decay rate of solutions. The case where the spacetime tends toward flat at a rate of $|x|^{-1}$ was studied by Tataru (2013), where a $t^{-3}$ pointwise decay rate was established. Here we extend the result to geometries tending toward flat at a rate of $|x|^{-kappa}$ and establish a pointwise decay rate of $t^{-kappa-2}$ for $kappainBbb{N}$ with $kappage 2$. We assume a weak local energy decay estimate holds, which restricts the geodesic trapping allowed on the underlying geometry. We use the resolvent to connect the time Fourier Transform of a solution to the Cauchy data. Ultimately the rate of pointwise wave decay depends on the low frequency behavior of the resolvent, which is sensitive to the rate at which the background geometry tends to flat.

abstract:

In this paper we continue the study of the defocusing, energy-subcritical nonlinear wave equation with radial initial data lying in the critical Sobolev space. In this case we prove scattering in the critical norm when $3<p<5$.

abstract:

We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems.

Abstract:

We prove that the moduli of stable supercurves with punctures is a smooth proper DM stack and study an analog of the Mumford's isomorphism for its canonical line bundle.

AMERICAN JOURNAL OF MATHEMATICS Founded in 1878 by Johns Hopkins University INDEX TO VOLUME 145 2023 PAGE AHLGREN, SCOTT, OLIVIA BECKWITH, and MARTIN RAUM. Scarcity of congruences for the partition function . . . . . . . . . . . . . . . . . . . . . . . . . . 1509 AISTLEITNER, CHRISTOPH, NICLAS TECHNAU, and AGAMEMNON ZAFEIROPOULOS. On the order of magnitude of Sudler products . 721 AN, XINLIANG, HAOYANG CHEN, and SILU YIN. Low regularity illposedness for elastic waves driven by shock formation . . . . . . . . . . . 1111 ASTORG, MATTHIEU and FABRIZIO BIANCHI. Hyperbolicity and bifurcations in holomorphic families of polynomial skew products. . . . . 861 BECKWITH, OLIVIA. See AHLGREN, SCOTT BELLAZZINI, JACOPO and DAVID RUIZ. Finite energy traveling waves for the Gross-Pitaevskii equation in the subsonic regime. . . . . . . . . . 109 BESAU, FLORIAN, THOMAS HACK, PETER PIVOVAROV, and FRANZ E. SCHUSTER. Spherical centroid bodies . . . . . . . . . . . . . . . . . . . . . . . . . . 515 BIANCHI, FABRIZIO. See ASTORG, MATTHIEU BONSANTE, FRANCESCO, GABRIELE MONDELLO, and JEAN-MARC SCHLENKER. Minimizing immersions of a hyperbolic surface in a hyperbolic 3-manifold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995 BRUCE, CHRIS and XIN LI. On K-theoretic invariants of semigroup C∗-algebras from actions of congruence monoids. . . . . . . . . . . . . . . . 251 BUIUM, ALEXANDRU and LANCE EDWARD MILLER. Perfectoid spaces arising from arithmetic jet spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 BULUT, AYNUR. Blow-up criteria below scaling for defocusing energysupercritical NLS and quantitative global scattering bounds. . . . . . . 543 CANTAT, SERGE, ANDRIY REGETA, and JUNYI XIE. Families of commuting automorphisms, and a characterization of the affine space . 413 CHAN, MELODY, CAREL FABER, SØREN GALATIUS, and SAM PAYNE. The Sn-equivariant top weight Euler characteristic of Mg,n . . . . . . 1549 CHEN, HAOJIE and WEIYI ZHANG. Kodaira dimensions of almost complex manifolds, I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 CHEN, HAOYANG. See AN, XINLIANG CHEN, SHIH-YU and ATSUSHI ICHINO. On Petersson norms of generic cusp forms and special values of adjoint L-functions for GSp4 . . . . 899 FABER, CAREL. See CHAN, MELODY FAOU, ERWAN and PIERRE RAPHAËL. On weakly turbulent solutions to the perturbed linear harmonic oscillator. . . . . . . . . . . . . . . . . . . . . . . . . 1465 FARAH, LUIZ GUSTAVO, JUSTIN HOLMER, SVETLANA ROUDENKO, and KAI YANG. Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation . . . . . . . . . . . . . . . . . . . . . . . . 1695 FELDER, GIOVANNI, DAVID KAZHDAN, and ALEXANDER POLISHCHUK . The moduli space of stable supercurves and its canonical line bundle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1777 FERNÁNDEZ, ISABEL, JOSÉ A. GÁLVEZ, and PABLO MIRA.

Abstract:

The critical CR GJMS operator on a strictly pseudoconvex CR manifold is a non-hypoelliptic CR invariant differential operator. We prove that, under the embeddability assumption, it is essentially self-adjoint and has closed range. Moreover, its spectrum is discrete, and the eigenspace corresponding to each non-zero eigenvalue is a finite-dimensional subspace of the space of smooth functions. As an application, we obtain a necessary and sufficient condition for the existence of a contact form with zero CR $Q$-curvature.

Abstract:

We prove that any complete, uniformly elliptic Weingarten surface in Euclidean $3$-space whose Gauss map image omits an open hemisphere is a cylinder or a plane. This generalizes a classical theorem by Hoffman, Osserman and Schoen for constant mean curvature surfaces. In particular, this proves that planes are the only complete, uniformly elliptic Weingarten multigraphs. We also show that this result holds for a large class of non-uniformly elliptic Weingarten equations. In particular, this solves in the affirmative the Bernstein problem for entire graphs for that class of elliptic equations. To obtain these results, we prove that planes are the only complete multigraphs with quasiconformal Gauss map and bounded second fundamental form.