Related papers: Sc-Smoothness, Retractions and New Models for Smoo…
This paper defines symplectic scale manifolds based on Hofer-Wysocki-Zehnder's scale calculus. We introduce Hamiltonian vector fields and flows on these by narrowing down sc-smoothness to what we denote by strong sc-smoothness, a concept…
Polyfold theory was developed by Hofer-Wysocki-Zehnder by finding commonalities in the analytic framework for a variety of geometric elliptic PDEs, in particular moduli spaces of pseudoholomorphic curves. It aims to systematically address…
In this paper we start with the applications of polyfold theory to symplectic field theory.
This survey wants to give a short introduction to the transversality problem in symplectic field theory and motivate to approach it using the new Fredholm theory by Hofer, Wysocki and Zehnder. With this it should serve as a lead-in for the…
We develop tools for the analysis of fronts, pulses, and wave trains in spatially extended systems with nonlocal coupling. We first determine Fredholm properties of linear operators, thereby identifying pointwise invertibility of the…
This paper is a self-contained presentation of certain aspects of the theory of weighted Sobolev spaces and elliptic operators on non-compact Riemannian manifolds. Specifically, we discuss (i) the standard and weighted Sobolev Embedding…
In this paper, we construct a Hamiltonian Floer theory based invariant called relative symplectic cohomology, which assigns a module over the Novikov ring to compact subsets of closed symplectic manifolds. We show the existence of…
Using tools and results from geometric measure theory, we give a simple new proof of the main result (Theorem 1.3) in K. Kondo and M. Tanaka, Approximation of Lipschitz Maps via Immersions and Differentiable Exotic Sphere Theorems,…
We consider homoclinic solutions for Hamiltonian systems in symplectic Hilbert spaces and generalise spectral flow formulas that were proved by Pejsachowicz and the author in finite dimensions some years ago. Roughly speaking, our main…
The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated…
We assign to each nondegenerate Hamiltonian on a closed symplectic manifold a Floer-theoretic quantity called its "boundary depth," and establish basic results about how the boundary depths of different Hamiltonians are related. As…
Multidimensional cosmological models in the presence of a bare cosmological constant and a perfect fluid are investigated under dimensional reduction to 4-dimensional effective models. Stable compactification of the internal spaces is…
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
In symplectic topology one uses elliptic methods to prove rigidity results about symplectic manifolds and solutions of Hamiltonian equations on them, where the most basic example is given by geodesics on Riemannian manifolds. Harmonic maps…
We give explicit Fredholm conditions for classes of pseudodifferential operators on suitable singular and non-compact spaces. In particular, we include a "user's guide" to Fredholm conditions on particular classes of manifolds including…
We introduce a class of functions near zero on the logarithmic cover of the complex plane that have convergent expansions into generalized power series. The construction covers cases where non-integer powers of $z$ and also terms containing…
We prove that the moduli space of gauge equivalence classes of symplectic vortices with uniformly bounded energy in a compact Hamiltonian manifold admits a Gromov compactification by polystable vortices. This extends results of Mundet i…
We study Sobolev type spaces defined in terms of sharp maximal functions on Ahlfors regular subsets of the Euclidean space and the relation between these spaces and traces of classical Sobolev spaces.
We develop the gluing theory of contact instantons in the context of open strings and in the context of closed strings \emph{with vanishing charge}, for example in the symplectization context. This is one of the key ingredients for the…
We study semiflows satisfying a certain squeezing condition with respect to a quadratic functional in some Banach space. Under certain compactness assumptions from our previous results it follows that there exists an invariant manifold,…