Si studiano le applicazioni -tangenti da a date come estensioni omogenee di -forme armoniche. Vengono ricavate condizioni necessarie sul grado affinche tali applicazioni -tangenti siano di energia minima. Una classificazione completa viene data nel caso in cui tali applicazioni tangenti di energia minima vadano da su .
We present several characterizations and representations of semi-complete vector fields on the open unit balls in complex Euclidean and Hilbert spaces.
The physical properties of particles and phasesare considered in connection with their description by means of the deformation of space-time. The analogy between particle trajectories and phase boundaries is discussed. The geometry and its curvature is related to the Clifford algebraic structure whose construction in terms of the theory of deformation leads to the expected solutions for correlation functions referring to spectroscopy and scattering problems. The stochastic nature of space-time is...
Après avoir enrichi la notion de connexion entre 1922 et 1925, Élie Cartan jette entre 1925 et 1930 les bases de l’étude topologique et géométrique globale des groupes de Lie et variétés homogènes. Nous voulons montrer que ce passage aux questions globales s’accompagne d’une réorganisation complète, aux niveaux théorique, thématique et rhétorique, autour d’une polarité local / global jusque là absente des travaux de Cartan ; elle remplace, selon nous, une polarité infinitésimal / fini héritée du...
We implement a singularity theory approach, the path formulation, to classify -equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a -miniversal unfolding of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of onto its unfolding parameter space. We apply our results to degenerate...
Given a metric space we consider a general class of functionals which measure the cost of a path in joining two given points and , providing abstract existence results for optimal paths. The results are then applied to the case when is aWasserstein space of probabilities on a given set and the cost of a path depends on the value of classical functionals over measures. Conditions for linking arbitrary extremal measures and by means of finite cost paths are given.
Let be a domain with smooth boundary and . A holomorphic function on is called a () peak function at if , , and for all . If is strongly pseudoconvex, then peak functions exist. On the other hand, J. E. Fornaess constructed an example in to show that this result fails, even for functions, on a weakly pseudoconvex domain [Math. Ann. 227, 173-175 (1977; Zbl 0346.32026)]. Subsequently, E. Bedford and J. E. Fornaess showed that there is always a continuous peak function on a...