http://www.openstarts.units.it:80/dspace/handle/10077/3314 Mon, 20 May 2013 16:21:30 GMT 2013-05-20T16:21:30Z http://www.openstarts.units.it:80/dspace/retrieve/9250/eut_logo_100_scritta.gif http://www.openstarts.units.it:80/dspace/handle/10077/3314 http://www.openstarts.units.it:80/dspace/handle/10077/8313 Title: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics Type: Fascicolo rivista Sun, 01 Jan 2012 00:00:00 GMT http://www.openstarts.units.it:80/dspace/handle/10077/8313 2012-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/8312 Title: On the supports for cohomology classes of complex manifolds Authors: Portelli, Dario Abstract: Let $X$ be a compact, connected complex manifold, and let $\xi\in H^{i}(X,{\mathbb Q} )$ be a non-trivial class. The paper deals with the possibility to construct a topological cycle $\Gamma$ on $X,$ whose class is the Poincar\'e dual of $\xi\thinspace ,$ which is closely related in a precise sense to the complex structure of $X.$ The desired properties of $\Gamma$ allow to define a differentiable relation into a suitable space of $1$-jets. This relation shows that there is a preliminary topological obstruction to construct such a $\Gamma$. The main result of the paper is that, in a relevant particular case, this obstruction disappears. Type: Articolo Sun, 01 Jan 2012 00:00:00 GMT http://www.openstarts.units.it:80/dspace/handle/10077/8312 2012-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/8311 Title: Infinitely many radial solutions of a mean curvature equation in Lorentz-Minkowski space Authors: Bonheure, Denis; De Coster, Colette; Derlet, Ann Abstract: In this paper, we show that the quasilinear equation $$ -{\rm div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u|^{2}}}\right) = |u|^{\alpha-2}u,\ \text{ in }\mathbb{R}^{N} $$ has a positive smooth radial solution at least for any $\alpha> 2^{\star}=2N/(N-2)$, $N\ge 3$. Our approach is based on the study of the optimizers for the best constant in the inequality $$ \int_{\mathbb{R}^N}(1-\sqrt{1-|\nabla u|^2}) \ge C \left( \int_{\mathbb{R}^{N}} |u|^\alpha\right)^{\frac{N}{\alpha+N}}, $$ which holds true in the unit ball of $W^{1,\infty}(\mathbb{R}^{{N}})\cap \mathcal D^{1;2}(\mathbb{R}^{N})$ if and only if $\alpha\ge 2^{\star}$. We also prove that the best constant is not achieved for $\alpha=2^{\star}$. As a byproduct, our arguments combined with Lusternik-Schnirelmann category theory allow to construct a sequence of radial solutions. Type: Articolo Sun, 01 Jan 2012 00:00:00 GMT http://www.openstarts.units.it:80/dspace/handle/10077/8311 2012-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/8307 Title: Katětov order, Fubini property and Hausdorff ultrafilters Authors: Hrušák, Michael; Meza-Alcántara, David Abstract: We study the Fubini property of ideals on omega and prove that the Solecki’s ideal S is critical for this property in the Katětov order. We show that a well-known F_sigma-ideal is critical for Hausdorff ultrafilters in the Katětov order and, by investigating the position of this ideal in the Katětov order, we show some of the known properties of this class of ultrafilters, including the Fubini property. Type: Articolo Sun, 01 Jan 2012 00:00:00 GMT http://www.openstarts.units.it:80/dspace/handle/10077/8307 2012-01-01T00:00:00Z