DSpace Collection:http://hdl.handle.net/10077/82542020-06-07T06:57:27Z2020-06-07T06:57:27ZRendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematicshttp://hdl.handle.net/10077/83132019-04-15T08:18:39Z2012-01-01T00:00:00ZTitle: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics2012-01-01T00:00:00ZOn the supports for cohomology classes of complex manifoldsPortelli, Dariohttp://hdl.handle.net/10077/83122019-03-02T06:42:16Z2012-01-01T00:00:00ZTitle: 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.2012-01-01T00:00:00ZInfinitely many radial solutions of a mean curvature equation in Lorentz-Minkowski spaceBonheure, DenisDe Coster, ColetteDerlet, Annhttp://hdl.handle.net/10077/83112019-03-02T06:33:46Z2012-01-01T00:00:00ZTitle: 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.2012-01-01T00:00:00ZKatětov order, Fubini property and Hausdorff ultrafiltersHrušák, MichaelMeza-Alcántara, Davidhttp://hdl.handle.net/10077/83072019-03-02T06:34:13Z2012-01-01T00:00:00ZTitle: 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.2012-01-01T00:00:00Z