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We define the category of manifolds with extended tangent bundles, we study their symmetries and we consider the analogue of equivariant cohomology for actions of Lie groups in this category. We show that when the action preserves the…

We prove a semi-invertible Oseledets theorem for cocycles acting on measurable fields of Banach spaces, i.e. we only assume invertibility of the base, not of the operator. As an application, we prove an invariant manifold theorem for…

We continue our investigation of versality for parametrized families of linear retarded functional differential equations (RFDEs) projected onto finite-dimensional invariant manifolds. In this paper, we consider RFDEs equivariant with…

By combining the ideas of Cartan's equivalence method and the method of the equivariant moving frame for pseudo-groups, we develop an efficient method for solving equivalence problems arising from horizontal Lie pseudo-group actions. The…

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…

In this paper we mainly investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed. We assume that the free surface is almost periodic in the horizontal direction. Using…

We study the topology of closed, simply-connected, 6-dimensional Riemannian manifolds of positive sectional curvature which admit isometric actions by $SU(2)$ or $SO(3)$. We show that their Euler characteristic agrees with that of the known…

Quasilinear systems with piecewise constant arguments of generalized type are under investigation from the asymptotic point of view. The systems have discontinuous right-hand sides which are identified via a discrete-time map. It is…

A topological invariant of the geodesic laminations on a modular surface is constructed. The invariant has a continuous part (the tail of a continued fraction) and a combinatorial part (the singularity data). It is shown, that the invariant…

This paper shows how left and right actions of Lie groups on a manifold may be used to complement one another in a variational reformulation of optimal control problems equivalently as geodesic boundary value problems with symmetry. We…

We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…

Consider a Hamiltonian action of a compact Lie group on a symplectic manifold which has the strong Lefschetz property. We establish an equivariant version of the Merkulov-Guillemin $d\delta$-lemma and an improved version of the…

We consider a family of spherical three dimensional spacelike slices embedded in the Schwarzschild solution. The mean curvature is constant on each slice but can change from slice to slice. We give a simple expression for an everywhere…

We give an extension of Cheeger's deformation techniques for smooth Lie group actions on manifolds to the setting of singular Riemannian foliations induced by Lie groupoids actions. We give an explicit description of the sectional curvature…

We determine when a quasi-isometry between discrete spaces is at bounded distance from a bilipschitz map. From this we prove a geometric version of the Von Neumann conjecture on amenability. We also get some examples in geometric groups…

We prove a cyclic Lefschetz formula for foliations. To this end, we define a notion of equivariant cyclic cohomology and show that its expected pairing with K-theory is well defined. This enables to associate to any invariant transverse…

We give a new and self-contained proof of the existence and unicity of the flow for an arbitrary (not necessarily homogeneous) smooth vector field on a real supermanifold, and extend these results to the case of holomorphic vector fields on…

In this work we consider a question in the calculus of variations motivated by riemannian geometry, the isoperimetric problem. We show that solutions to the isoperimetric problem, close in the flat norm to a smooth submanifold, are…

We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hypersurfaces are critical points of the fractional perimeter under a volume constraint. We use local inversion arguments to prove existence of…

The recent Reply by Oberlack et al. [Phys. Rev. Lett. 130, 069403 (2023)] fails to rebut the critique that a mathematical solution method has been misapplied in their original work. On a point-by-point basis we prove that all arguments put…