Mathematische Annalen最新文献

Study design: Retrospective chart review.

Objective: Restoration of premorbid occlusion is a key goal in the treatment of mandibular fractures. Placement of the patient in maxillomandibular fixation (MMF) is performed during mandibular fracture repair to help establish occlusion. A number of techniques are available to achieve MMF. We sought to examine trends in MMF technique at our institution.

Methods: A retrospective chart review was conducted to evaluate patients who underwent surgical treatment of mandibular fractures between January 1, 2011 and March 31, 2021. Data including fracture characteristics, mechanism of injury, patient demographics, complication rates, and MMF technique utilized were collected.

Results: One hundred sixty-three patients underwent MMF (132 males). The most common etiology of fracture was assault (34%). There was an increasing preference for rapid MMF techniques over time, as opposed to standard Erich arch bars. No significant difference in obtaining adequate fracture reduction as determined by postoperative imaging or complications were noted between those who underwent MMF with newer rapid techniques vs traditional MMF techniques.

Conclusions: Our institution has demonstrated changing trends in the technique utilized for establishing occlusion intraoperatively, more recently favoring rapid MMF techniques, with similar rates of complications and ability to adequately reduce fractures.

We prove the existence of the weak solutions to the compressible Navier–Stokes system with barotropic pressure (p(varrho )=varrho ^gamma ) for (gamma ge 9/5) in three space dimension. The novelty of the paper is the approximation scheme that instead of the classical regularization of the continuity equation (based on the viscosity approximation (varepsilon Delta varrho )) uses more direct truncation and regularisation of nonlinear terms and the pressure. This scheme is compatible with the Bresch–Jabin compactness criterion for the density. We revisit this criterion and prove, in full rigour, that it can be applied in our approximation at any level.

We study compressible nematic liquid crystal flows with the bulk viscosity being a power function of the density ((lambda =rho ^beta )) on the whole two-dimensional (2D) plane. Under a geometric angle condition for the initial direction field, we show the global existence and uniqueness of strong solutions provided that (beta >frac{4}{3}). It should be noticed that there is no other restrictions on the size of initial data and the initial density allows vacuum states.

In this article, we investigate systems of generalized Schrödinger operators and their fundamental matrices. More specifically, we establish the existence of such fundamental matrices and then prove sharp upper and lower exponential decay estimates for them. The Schrödinger operators that we consider have leading coefficients that are bounded and uniformly elliptic, while the zeroth-order terms are assumed to be nondegenerate and belong to a reverse Hölder class of matrices. In particular, our operators need not be self-adjoint. The exponential bounds are governed by the so-called upper and lower Agmon distances associated to the reverse Hölder matrix that serves as the potential function. Furthermore, we thoroughly discuss the relationship between this new reverse Hölder class of matrices, the more classical matrix ({mathcal {A}_{p,infty }}) class, and the matrix ({mathcal {A}_infty }) class introduced by Dall’Ara (J Funct Anal 268(12):3649–3679, 2015).

The triangulation complexity of a compact 3-manifold M is the minimal number of tetrahedra in any triangulation of M. We compute the triangulation complexity of all elliptic 3-manifolds and all sol 3-manifolds, to within a universally bounded multiplicative error.

Abstract

Let S be either a free group or the fundamental group of a closed hyperbolic surface. We show that if G is a finitely generated residually-p group with the same pro-p completion as S, then two-generated subgroups of G are free. This generalises (and gives a new proof of) the analogous result of Baumslag for parafree groups. Our argument relies on the following new ingredient: if G is a residually-(torsion-free nilpotent) group and (Hle G) is a virtually polycyclic subgroup, then H is nilpotent and the pro-p topology of G induces on H its full pro-p topology. Then we study applications to profinite rigidity. Remeslennikov conjectured that a finitely generated residually finite G with profinite completion ({hat{G}}cong {hat{S}}) is necessarily (Gcong S) . We confirm this when G belongs to a class of groups ({mathcal {H}_textbf{ab}}) that has a finite abelian hierarchy starting with finitely generated residually free groups. This strengthens a previous result of Wilton that relies on the hyperbolicity assumption. Lastly, we prove that the group (Stimes mathbb {Z}^n) is profinitely rigid within finitely generated residually free groups.

Abstract

In this paper, we prove an intersection-theoretic result pertaining to curves in certain Hilbert modular surfaces in positive characteristic p. Specifically, let C, D be two proper curves inside a mod p Hilbert modular surface associated to a real quadratic field split at p. Suppose that the curves are generically ordinary, and that at least one of them is ample. Then, the set of points in ((x,y) in Ctimes D) with abelian surfaces parameterized by x and y isogenous to each other is Zariski dense in (Ctimes D) , thereby proving a case of a just-likely intersection conjecture. We also compute the change in Faltings height under appropriate p-power isogenies of abelian surfaces with real multiplication over characteristic p global fields.

Given a closed four-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in (X {setminus } smash {mathring{B}^4}), with boundary a knot (K subset S^3). We give several methods to bound the genus of such surfaces in a fixed homology class. Our tools include adjunction inequalities and the (10/8 + 4) theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disk) in a four-manifold and show that the set of H-slice knots can detect exotic smooth structures on closed 4-manifolds.

We prove limit theorems for the homological winding of geodesic rays distributed via a harmonic measure on a Gromov hyperbolic space. We obtain applications to the inverse problem for the harmonic measure, and winding statistics for Patterson–Sullivan measures.

The aim of this paper is to obtain the optimal characterizations of locations for all nodes of the classical Sturm-Liouville operators, given the (L^p) norms with (1<p <infty ) of the potentials. Regarding the ith node of the mth eigenfunction as a functional of the potential, we deduce critical equations to determine the minimizing potential such that the node is minimized. From the critical equations, we obtain two equivalent characterizations of the minimal nodes, which are written as nonlinear systems for 4-dimensional or 2-dimensional parameters. These optimal characterizations can yield the sharp lower and upper bounds for the locations of nodes.