2 citations · 3 across the 4 of their papers we have counts for
7 papers
Quantitative symplectic geometry
K. Cieliebak, H. Hofer, J. Latschev +1
While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacit…
A note on mean curvature, Maslov class and symplectic area of Lagrangian immersions
Kai Cieliebak, Edward Goldstein
In this note we prove a simple relation between the mean curvature form, symplectic area, and the Maslov class of a Lagrangian immersion in a Kähler-Einstein manifold. An immediate…
Symplectic homology and periodic orbits near symplectic submanifolds
Kai Cieliebak, Viktor L. Ginzburg, Ely Kerman
We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has non-vanishing symplectic homology. As a consequen…
Wall crossing for symplectic vortices and quantum cohomology
Kai Cieliebak, Dietmar A. Salamon
We derive a wall crossing formula for the symplectic vortex invariants of toric manifolds. As an application, we give a proof of Batyrev's formula for the quantum cohomology of a m…
Subcritical Stein manifolds are split
Kai Cieliebak
It is shown that every subcritical Stein manifold is deformation equivalent to the product of a Stein manifold with $\C$.
The symplectic vortex equations and invariants of Hamiltonian group actions
Kai Cieliebak, A. Rita Gaio, Ignasi Mundet i Riera +1
In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambi…