Related papers: Morse homology for a class of elliptic partial dif…

In this paper we show how to construct Morse homology for an explicit class of functionals involving the $p$-Laplacian. The natural domain of definition of such functionals is the Banach space $W^{1,2p}_0(\Omega)$, where $p>n/2$ and $\Omega…

In this paper we lay the foundations for the Morse theoretical study of strongly indefinite functionals on Banach manifolds by developing the local theory for a specific model class that captures several key analytical features also arising…

Let $(M,\bar g)$ be a compact Riemannian manifold with minimal boundary such that the second fundamental form is nowhere vanishing on $\partial M$. We show that for a generic Riemannian metric $\bar g$, the squared norm of the second…

In this paper we prove a Morse Lemma for degenerate critical points of a function u which satisfies -\Delta u=f(u) in B_1, where B_1 is the unit ball of R^2 and f is a smooth nonlinearity. Other results on the nondegeneracy of the critical…

The Gromoll-Meyer's generalized Morse lemma (so called splitting lemma) near degenerate critical points on Hilbert spaces, which is one of key results in infinite dimensional Morse theory, is usually stated for at least $C^2$-smooth…

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Based on an idea of B. White, we…

The usual Gromoll-Meyer's generalized Morse lemma near degenerate critical points on Hilbert spaces, so called splitting lemma, is stated for at least $C^2$-smooth functionals. In this paper we establish a splitting theorem and a shifting…

We describe an extension of Morse theory to smooth functions on compact Riemannian manifolds, without any nondegeneracy assumptions except that the critical locus must have only finitely many connected components.

We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type…

In this paper we construct coherent states for the two-dimensional Morse potential. We find the dependence of the spectrum on the physical parameters and use this to understand the emergence of accidental degeneracies. It is observed that,…

We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type…

In this paper, we construct local Morse homology in a new way and compute the local Morse homology of the critical points of the Lagrange problem. As a corollary, we prove for the first time that each of the linear critical points is either…

We propose a Hodge theory for the spaces $E_2^{p,\,q}$ featuring at the second step either in the Fr\"olicher spectral sequence of an arbitrary compact complex manifold $X$ or in the spectral sequence associated with a pair $(N,\,F)$ of…

On a smooth manifold, we associate to any closed differential form a mapping cone complex. The cohomology of this mapping cone complex can vary with the de Rham cohomology class of the closed form. We present a novel Morse theoretical…

We study the critical points of the solution of second elliptic equations in divergence and diagonal form with a bounded and positive definite coefficient, under the assumption that the statement of the Hopf lemma holds (sign assumptions on…

We give some generic properties of non degeneracy for critical points of functionals. We apply these results, obtaining some theorems of multiplicity of solutions for the equation -{\epsilon}^2\Delta_g u+u=|u|p-2u in M, u in H_g^1(M) where…

Let $Y\subseteq \mathbb{R}^n$ be a closed definable subset and $X\subseteq \mathbb{R}^n$ be a smooth manifold. We construct a version of Morse theory for the restriction to $X$ of the Euclidean distance function from $Y$. This is done using…

In this note we study the global regularity in the Morrey spaces for the second derivatives for the strong solutions of non variational elliptic equations.

We show a result of genericity for non degenerate critical points of the Robin function with respect to deformations of the domain

In this paper we introduce Morse Lie groupoid morphisms and study their main properties. We show that this notion is Morita invariant which gives rise to a well defined notion of Morse function on differentiable stacks. We show a groupoid…