Remarks on an eigenvalue problem associated with the -Laplace operator.
We obtain rigidity and gluing results for the Morse complex of a real-valued Morse function as well as for the Novikov complex of a circle-valued Morse function. A rigidity result is also proved for the Floer complex of a hamiltonian defined on a closed symplectic manifold with . The rigidity results for these complexes show that the complex of a fixed generic function/hamiltonian is a retract of the Morse (respectively Novikov or Floer) complex of any other sufficiently close generic function/hamiltonian....
This article follows the previous works [HeKlNi, HeNi] by Helffer-Klein-Nier and Helffer-Nier about the metastability in reversible diffusion processes via a Witten complex approach. Again, exponentially small eigenvalues of some self-adjoint realization of are considered as the small parameter tends to . The function is assumed to be a Morse function on some bounded domain with boundary . Neumann type boundary conditions are considered. With these boundary conditions, some possible simplifications...
We discuss the existence of closed geodesic on a Riemannian manifold and the existence of periodic solution of second order Hamiltonian systems.
We present critical groups estimates for a functional defined on the Banach space , bounded domain in , , associated to a quasilinear elliptic equation involving -laplacian. In spite of the lack of an Hilbert structure and of Fredholm property of the second order differential of in each critical point, we compute the critical groups of in each isolated critical point via Morse index.