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$p$ -minimising tangent maps and harmonic $k$ -forms

Stefano Montaldo (1999)

Bollettino dell'Unione Matematica Italiana

Si studiano le applicazioni $p$ -tangenti da $R^{m}$ a $S^{n}$ date come estensioni omogenee di $k$ -forme armoniche. Vengono ricavate condizioni necessarie sul grado $k$ affinche tali applicazioni $p$ -tangenti siano di energia minima. Una classificazione completa viene data nel caso in cui tali applicazioni tangenti di energia minima vadano da $R^{8}$ su $S^{4}$ .

Packing dimensions, transversal mappings and geodesic flows.

Leikas, Mika (2004)

Annales Academiae Scientiarum Fennicae. Mathematica

Paracomplex projective models and harmonic maps into them.

Erdem, Sadettin (1999)

Beiträge zur Algebra und Geometrie

Parallelizability in Banach spaces: parallelizable dynamical systems with bounded trajectories

Barnabas M. Garay (1989)

Banach Center Publications

Parametric homotopy principle of some partial differential relations

Mahuya Datta, Amiya Mukherjee (1998)

Mathematica Slovaca

Parametric representations of semi-complete vector fields on the unit balls in $C^{n}$ and in Hilbert space

Dov Aharonov, Mark Elin, Simeon Reich, David Shoikhet (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We present several characterizations and representations of semi-complete vector fields on the open unit balls in complex Euclidean and Hilbert spaces.

Paramétrix de l'équation des ondes et intégrales sur l'espace des chemins

Y. Colin de Verdière (1974/1975)

Séminaire Équations aux dérivées partielles (Polytechnique)

Paramétrix d’opérateurs elliptiques de classe $C^{μ}$

Marc Durand (1975)

Bulletin de la Société Mathématique de France

Paramétrix pour un problème de Cauchy hyperbolique à multiplicité variable

S. Alinhac (1975/1976)

Séminaire Équations aux dérivées partielles (Polytechnique)

Parbolic pseudo-differential initial-boundary value problems.

Veikko T. Purmonen (1989)

Mathematica Scandinavica

Partial compactness for the 2-D Landau-Lifshitz flow.

Harpes, Paul (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Partial differential analogs of ordinary differential equations and systems.

Hakopian, Hakop A., Tonoyan, Mariam G. (2004)

The New York Journal of Mathematics [electronic only]

Partial regularity results up to the boundary for harmonic maps into a Finsler manifold

Atsushi Tachikawa (2009)

Annales de l'I.H.P. Analyse non linéaire

Particles, phases, fields

L. Wojtczak, A. Urbaniak-Kucharczyk, I. Zasada, J. Rutkowski (1996)

Banach Center Publications

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...

Passer au global : le cas d’Élie Cartan, 1922–1930

Renaud Chorlay (2009)

Revue d'histoire des mathématiques

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...

Path formulation for multiparameter $𝔻_{3}$ -equivariant bifurcation problems

Jacques-Élie Furter, Angela Maria Sitta (2010)

Annales de l’institut Fourier

We implement a singularity theory approach, the path formulation, to classify $𝔻_{3}$ -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 $𝔻_{3}$ -miniversal unfolding $F_{0}$ of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of $F_{0}$ onto its unfolding parameter space. We apply our results to degenerate...

Path functionals over Wasserstein spaces

Alessio Brancolini, Giuseppe Buttazzo, Filippo Santambrogio (2006)

Journal of the European Mathematical Society

Given a metric space $X$ we consider a general class of functionals which measure the cost of a path in $X$ joining two given points $x_{0}$ and $x_{1}$ , providing abstract existence results for optimal paths. The results are then applied to the case when $X$ is aWasserstein space of probabilities on a given set $Ω$ and the cost of a path depends on the value of classical functionals over measures. Conditions for linking arbitrary extremal measures $μ_{0}$ and $μ_{1}$ by means of finite cost paths are given.

Path integrals in finite sets

Erik G. F. Thomas (1994)

Acta Universitatis Carolinae. Mathematica et Physica

PDI&PDE-constrained optimization problems with curvilinear functional quotients as objective vectors.

Pitea, Ariana, Udrişte, Constantin, Mititelu, Ştefan (2009)

Balkan Journal of Geometry and its Applications (BJGA)

Peak functions on convex domains

Kolář, Martin (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

Let $Ω \subset ℂ^{n}$ be a domain with smooth boundary and $p \in \partial Ω$ . A holomorphic function $f$ on $Ω$ is called a $C^{k}$ ( $k = 0, 1, 2, \dots$ ) peak function at $p$ if $f \in C^{k} (\bar{Ω})$ , $f (p) = 1$ , and $| f (q) | < 1$ for all $q \in \bar{Ω} ∖ {p}$ . If $Ω$ is strongly pseudoconvex, then $C^{\infty}$ peak functions exist. On the other hand, J. E. Fornaess constructed an example in $ℂ^{2}$ to show that this result fails, even for $C^{1}$ 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...

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