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Artykuły w czasopismach na temat "Théorème des métriques bosselées"
Pelletier, Fernand. "Sur le théorème de Gauss-Bonnet pour les pseudo-métriques singulières". Séminaire de théorie spectrale et géométrie 5 (1987): 99–105. http://dx.doi.org/10.5802/tsg.44.
Pełny tekst źródłaRandriambololona, Hugues. "Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents". Journal fur die reine und angewandte Mathematik (Crelles Journal) 2006, nr 590 (26.01.2006). http://dx.doi.org/10.1515/crelle.2006.004.
Pełny tekst źródłaRozprawy doktorskie na temat "Théorème des métriques bosselées"
Berthomieu, Alain. "Métriques de Quillen et suite spectrale de Leray". Paris 11, 1993. http://www.theses.fr/1993PA112199.
Pełny tekst źródłaYi, Li. "Théorèmes d'extension et métriques de Kähler-Einstein généralisées". Thesis, Université de Lorraine, 2012. http://www.theses.fr/2012LORR0151/document.
Pełny tekst źródłaThis thesis consists in two parts: -In the first part, we first deal with a Kahler version of the famous Ohsawa-Takegoshi extension theorem; then, a problem of extending the closed positive currents. Our motivation comes from the Siu's conjecture on the invariance of plurigenera over a Kahler family. Indeed, in the proof of his famous theorem, the Ohsawa-Takegoshi theorem plays an important role. It is, therefore, natural to think that the proof for the conjecture involves an extension theorem of Ohsawa-Takegoshi type in the Kahler case. Because of the technical difficulties coming from the regularization process of quasi-psh functions over the compact Kahler manifolds, we only obtain two special cases of the hoped result. As for the extension of closed positive currents, our result is a special case of the conjecture which predicts that every closed positive current defined over the central fiber in a Kahler cohomology class twisted by the first Chern class of the canonical bundle admits an extension. -In the second part, we are interested in the uniqueness of the solutions of the equations of generalized Monge-Ampère type, a generalized Bando-Mabuchi theorem concerning the Kahler-Einstein metrics over Fano manifolds. We follow the method introduced by Berndtsson and generalize his result by working with a closed positive current in place of a klt pair in his context. The properties of the convexity of the Bergman metrics play an important role in this part
Kozhevnikov, Artem. "Propriétés métriques des ensembles de niveau des applications différentiables sur les groupes de Carnot". Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112073/document.
Pełny tekst źródłaMetric properties of level sets of differentiable maps on Carnot groupsAbstract.We investigate the local metric properties of level sets of mappings defined between Carnot groups that are horizontally differentiable, i.e.with respect to the intrinsic sub-Riemannian structure. We focus on level sets of mapping having a surjective differential,thus, our study can be seen as an extension of implicit function theorem for Carnot groups.First, we present two notions of tangency in Carnot groups: one based on Reifenberg's flatness condition and another coming from classical convex analysis.We show that for both notions, the tangents to level sets coincide with the kernels of horizontal differentials.Furthermore, we show that this kind of tangency characterizes the level sets called ``co-abelian'', i.e.for which the target space is abelian andthat such a characterization may fail in general.This tangency result has several remarkable consequences.The most important one is that the Hausdorff dimension of the level sets is the expected one. We also show the local connectivity of level sets and, the fact that level sets of dimension one are topologically simple arcs.Again for dimension one level set, we find an area formula that enables us to compute the Hausdorff measurein terms of generalized Stieltjes integrals.Next, we study deeply a particular case of level sets in Heisenberg groups. We show that the level sets in this case are topologically equivalent to their tangents.It turns out that the Hausdorff measure of high-codimensional level sets behaves wildly, for instance, it may be zero or infinite.We provide a simple sufficient extra regularity condition on mappings that insures Ahlfors regularity of level sets.Among other results, we obtain a new general characterization of Lipschitz graphs associated witha semi-direct splitting of a Carnot group of arbitrary step.We use this characterization to derive a new characterization of co-ablian level sets that can be represented as graphs
Mehidi, Lilia. "Points conjugués des tores lorentziens". Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0295.
Pełny tekst źródłaIn the first part of this thesis, we give a description of simply connected maximal Lorentzian surfaces whose group of isometries is of dimension 1 (i.e. with a complete Killing field), in terms of a 1-dimensional generally non-Hausdorff Riemannian manifold and a smooth function defined there. Next, we study the geodesic completeness of such surfaces. In the second part which is the main part of this thesis, we give infinitely many new examples of compact Lorentzian surfaces without conjugate points. Further, we study the existence and the stability of this property among Lorentzian metrics with a Killing field. We obtain a new obstruction and prove that the Clifton- Pohl torus and some of our examples are as stable as possible. This shows that in constrast with the Riemannian Hopf theorem, the absence of conjugate points in the Lorentzian setting is neither "special" nor rigid