Related papers: Wermer examples and currents
Let (F_n) be a sequence of (multivalued) meromorphic maps between compact Kaehler manifolds X1 and X2. We study the asymptotic distribution of preimages of points by F_n and the asymptotic distribution of fixed points for multivalued…
The relation between the trace and R-current anomalies in supersymmetric theories implies that the U$(1)_RF^2$, U$(1)_R$ and U$(1)_R^3$ anomalies which are matched in studies of N=1 Seiberg duality satisfy positivity constraints. Some…
We consider nonlinear Schrodinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding…
Self-similar curves arise naturally as the tension-free equilibrium states of conformally invariant bending energies. The simplest example is the M\"obius invariant conformal arc-length on planar curves, dependent on the Frenet curvature…
We establish the existence of loop type subcontinua of nonnegative solutions for a class of concave-convex type elliptic equations with indefinite weights, under Dirichlet and Neumann boundary conditions. Our approach depends on local and…
In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are perturbations of annular equilibria, in contrast to the laminar…
Investigations of scattering in presence of non-linearity which have just begun require the confinement of both the potential, $V(x)$, and the non-linearity, $\gamma f(|\psi|)$. There could be two options for the confinement. One is the…
We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum…
In this paper we study the local regularity of closed surfaces immersed in a Riemannian 3-manifold flowing by Willmore flow. We establish a pair of concentration-compactness alternatives for the flow, giving a lower bound on the maximal…
We study the fine geometric structure of bifurcation currents in the parameter space of cubic polynomials viewed as dynamical systems. In particular we prove that these currents have some laminar structure in a large region of parameter…
We present a proof that the currents arising from Noether's first theorem in a physical theory with local invariance can always be decomposed into two terms, one of them vanishing on-shell, and the other having an off-shell vanishing…
Let $T$ be a positive closed current of bidimension $(p,p)$ with unit mass on the complex projective space $\mathbb P^n$. For certain values of $\alpha$ and $\beta = \beta(p, \alpha)$ we show that if $T$ has enough points where the Lelong…
We prove various uniqueness results from null infinity, for linear waves on asymptotically flat space-times. Assuming vanishing of the solution to infinite order on suitable parts of future and past null infinities, we derive that the…
In this note, as a particular case of a more general result, we obtain the following theorem: Let $\Omega\subseteq {\bf R}^n$ be a non-empty bounded open set and let $f:\overline {\Omega}\to {\bf R}^n$ be a continuous function which is…
Continuing the discussion on negative entropy in Casimir-effect like configurations, we consider two simple one-dimensional examples. One is the s-wave contribution to a plasma sphere and the other a single delta function potential. Some…
We describe how a stable effective theory in which particles of the same fermion number attract may spontaneously break Lorentz invariance by giving non-zero fermion number density to the vacuum (and therefore dynamically generating a…
On any closed Riemannian manifold of dimension greater than $7$, we construct examples of background physical coefficients for which the Einstein-Lichnerowicz equation possesses a non-compact set of positive solutions. This yields in…
The initial value problem for some coupled nonlinear Schrodinger system with unbounded potential is investigated. In the defocusing case, global well-posedness is obtained. For the focusing sign, existence of global and non global solutions…
The aim of this article is to enlarge the list of examples of non-autonomous basins of attraction from our previous paper and at the same time explore some other properties that they satisfy. For instance, we show the existence of countably…
We study (strong) first countability of locally solid convergence structures on Archimedean vector lattices. Among other results, we characterise those vector lattices for which relatively unform-, order-, and $\sigma$-order convergence,…