Let (M,L) be a polarized threefold of log-general type. The birationality of the bicanonical map of a smooth surface S ∈ |L| is studied. This problem was previously considered and partially solved by the first and fourth author, who gave a satisfactory classification unless h(OM) = 0 and pg(S) = 3, 4, 5. This paper focuses on the remaining cases which are the hardest, settling the problem. Intr...

Abstract In this paper we study quasilinear elliptic equations driven by the double phase operator and a right-hand side which has combined effect of singular parametric term. Based on fibering method using Nehari manifold are going to prove existence at least two weak solutions for such problems when parameter is sufficiently small.

This paper describes some properties of a certain fibered hyperbolic 3manifold which arises ”in nature”; that is, as the cover of a closed manifold constructed by other means. Among other things, the main theorem answers in the affirmative the question of whether it is possible for a fibered hyperbolic manifold to be a double across a connected surface. (We first heard this question from Alan R...

The purpose of this work is to analyze mathematical models describing the behavior of individuals inhabiting an environment with spatial heterogeneity. The latter means that the environment influences the reproductivity and mobility of the species. This effect is obtained if we model the density function of these organisms by evolution partial differential equations with nonconstant coefficient...

We study a twisted Alexander polynomial naturally associated to a hyperbolic knot in an integer homology 3-sphere via a lift of the holonomy representation to SL(2,C). It is an unambiguous symmetric Laurent polynomial whose coefficients lie in the trace field of the knot. It contains information about genus, fibering, and chirality, and moreover is powerful enough to sometimes detect mutation. ...

In the paper [L] a project for proving the existence of transfer factors for forms of SL(3), especially for the unitary groups studied by Rogawski, was begun, and it was promised that it would be completed by the present authors. Their paper is still in the course of being written, but the present essay can serve as an introduction to it. It deals with SL(2) which has, of course, already been d...

Under certain homological hypotheses on a compact 4-manifold, we prove exactness of the topological surgery sequence at the stably smoothable normal invariants. This technical result allows an extension of Cappell’s 5-dimensional splitting theorem. As an application, we analyze, up to internal s-cobordism, the splitting and fibering problems for certain 5-manifolds mapping to the circle. For ex...