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Let $P (M, G)$ be a principal fiber bundle and $E (M, N, G, P)$ an associated fiber bundle. Our interest is to study the harmonic sections of the projection $π_{E}$ of $E$ into $M$ . Our first purpose is give a characterization of harmonic sections of $M$ into $E$ regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of $π_{E}$ .

A characterization of the eigenvalues of a completely continuous selfadjoint operator

Joachim Naumann (1972)

Commentationes Mathematicae Universitatis Carolinae

A characterization of the Riemann extension in terms of harmonicity

Cornelia-Livia Bejan, Şemsi Eken (2017)

Czechoslovak Mathematical Journal

If $(M, \nabla)$ is a manifold with a symmetric linear connection, then $T^{*} M$ can be endowed with the natural Riemann extension $\bar{g}$ (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to $\bar{g}$ initiated by C. L. Bejan and O. Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure $𝒫$ on $(T^{*} M, \bar{g})$ and prove that $𝒫$ is harmonic (in the sense of E. García-Río, L. Vanhecke and M. E. Vázquez-Abal (1997)) if and only if $\bar{g}$ reduces to the...

A classification and some constructions of $p$ -harmonic morphisms.

Ou, Ye-Lin, Wei, Shihshu Walter (2004)

Beiträge zur Algebra und Geometrie

A compactness theorem of n-harmonic maps

Chang You Wang (2005)

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

A critical point result for non-differentiable indefinite functionals

Salvatore A. Marano, Dumitru Motreanu (2004)

Commentationes Mathematicae Universitatis Carolinae

In this paper, two deformation lemmas concerning a family of indefinite, non necessarily continuously differentiable functionals are proved. A critical point theorem, which extends the classical result of Benci-Rabinowitz [14, Theorem 5.29] to the above-mentioned setting, is then deduced.

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$ℤ_{2}$ -equivariant Ljusternik-Schnirelman theory for non-even functionals

$𝒟$ -modules, contact valued calculus and Poincaré-Cartan form

2- I Inégalités faibles de Morse

2- II Inégalités fortes de Morse

2 Inégalités de Morse d'après E. Witten

517.98

A bifurcation result for equations with anisotropic $p$ -Laplace-like operators.

A "Birkhoff-Lewis" type result for a class of Hamiltonian systems.

A characterization of harmonic sections and a Liouville theorem

A characterization of the eigenvalues of a completely continuous selfadjoint operator

A characterization of the Riemann extension in terms of harmonicity

A classification and some constructions of $p$ -harmonic morphisms.

A compactness theorem of n-harmonic maps

A critical point result for non-differentiable indefinite functionals

A Cyclic Projection Algorithm Via Duality.

A double eigenvalue problem for Schrödinger equations involving sublinear nonlinearities at infinity.

A few symmetry results for nonlinear elliptic PDE on noncompact manifolds

A finiteness theorem of harmonic maps form compact Lie groups to OHS(H).

A framework for Morse theory for the Yang-Mills functional.

A free boundary problem involving limiting Sobolev exponents.

Currently displaying 1 – 20 of 1170