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Some results on critical groups for a class of functionals defined on Sobolev Banach spaces

Silvia Cingolani, Giuseppina Vannella (2001)

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

We present critical groups estimates for a functional f defined on the Banach space W 0 1 , p Ω , Ω bounded domain in R N , 2 < p < , associated to a quasilinear elliptic equation involving p -laplacian. In spite of the lack of an Hilbert structure and of Fredholm property of the second order differential of f in each critical point, we compute the critical groups of f in each isolated critical point via Morse index.

Some results on curvature and topology of Finsler manifolds

Bing Ye Wu (2013)

Annales Polonici Mathematici

We investigate the curvature and topology of Finsler manifolds, mainly the growth of the fundamental group. By choosing a new counting function for the fundamental group that does not rely on the generators, we are able to discuss the topic in a more general case, namely, we do not demand that the manifold is compact or the fundamental group is finitely generated. Among other things, we prove that the fundamental group of a forward complete and noncompact Finsler n-manifold (M,F) with nonnegative...

Some special geometry in dimension six

Čap, Andreas, Eastwood, Michael (2003)

Proceedings of the 22nd Winter School "Geometry and Physics"

Motivated by the study of CR-submanifolds of codimension  2 in  4 , the authors consider here a 6 -dimensional oriented manifold  M equipped with a 4 -dimensional distribution. Under some non-degeneracy condition, two different geometric situations can occur. In the elliptic case, one constructs a canonical almost complex structure on  M ; the hyperbolic case leads to a canonical almost product structure. In both cases the only local invariants are given by the obstructions to integrability for these structures....

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