Related papers: Singular equivariant asymptotics and the moment ma…
We compute the asymptotic for the eigenvalues of a particular class of compact operators deeply linked with the second variation of optimal control problems. We characterize this family in terms of a set of finite dimensional data and we…
Cohomogeneity one actions on irreducible Riemannian symmetric spaces of compact type are classified into three cases: Hermann actions, actions induced by the linear isotropy representation of a Riemannian symmetric space of rank 2, and…
In this paper, we recall some general properties and theorems about Translating Solitons in Semi Riemannian Manifolds. Moreover, we investigate those which are invariant by the action of a Lie group of isometries of the ambient space, by…
This text presents some basic notions in symplectic geometry, Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentum maps and their use for the reduction of Hamiltonian…
We introduce and study a new spectral sequence associated with a Poisson group action on a Poisson manifold and an equivariant momentum mapping. This spectral sequence is a Poisson analog of the Leray spectral sequence of a fibration. The…
The main results of this article provide asymptotics at infinity of the Green's functions near and at the spectral gap edges for "generic" periodic second-order elliptic operators on noncompact Riemannian co-compact coverings with abelian…
Using symplectic techniques and spectral analysis of smooth paths of self-adjoint operators, we characterize the set of conjugate instants along a geodesic in an infinite dimensional Riemannian Hilbert manifold.
This note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new result for nonexpansive maps of $\ell^{1}$. We also point…
In this expository article, we consider first order elliptic differential operators acting on smooth vector bundles over compact manifolds, and certain invariants derived from the analysis of these operators, namely the eta invariant} and…
We introduce the notion of a weak (homotopy) moment map associated to a Lie group action on a multisymplectic manifold. We show that the existence/uniqueness theory governing these maps is a direct generalization from symplectic geometry.…
This paper is twofold. The first part aims to study the long-time asymptotic behavior of solutions to the heat equation on Riemannian symmetric spaces $G/K$ of noncompact type and of general rank. We show that any solution to the heat…
We study asymptotic behavior in a class of non-autonomous second order parabolic equations with time periodic unbounded coefficients in $\mathbb R\times \mathbb R^d$. Our results generalize and improve asymptotic behavior results for Markov…
We study the family of holomorphic maps from the polydisk to the disk which restrict to the identity on the diagonal. In particular, we analyze the asymptotics of the orbit of such a map under the conjugation action of a unipotent subgroup…
A generalized moment map is proposed for arbitrary symplectic actions of compact connected Lie groups on closed symplectic manifolds, in the spirit of the circle -valued maps introduced by D. McDuff in the case of non-Hamiltonian circle…
We study spectral properties of second order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with either Dirichlet, or Neumann, or the third boundary condition.…
We give some sufficient conditions for preserving of the second term in the spectral asymptotics of a compact operator under the perturbation of the metrics in the Hilbert space.
We prove equivariant spectral asymptotics for $ h$-pseudodifferential operators for compact orthogonal group actions generalizing results of El-Houakmi and Helffer (1991) and Cassanas (2006). Using recent results for certain oscillatory…
In this paper we extend the results of Kirwan et alii on convexity properties of the moment map for Hamiltonian group actions, and on the connectedness of the fibers of the moment map, to the case of non-compact orbifolds. Our motivation is…
Suppose that a compact and connected Lie group $G$ acts on a complex Hodge manifold $M$ in a holomorphic and Hamiltonian manner, and that the action linearizes to a positive holomorphic line bundle $A$ on $M$. Then there is an induced…
We prove an equivariant Lefschetz formula for elliptic complexes over a compact manifold carrying the action of a compact Lie group of isometries via heat equation methods.