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In this short note we observe that the boundary of a properly embedded compact exact Lagrangian sub-manifolds in a subcritical Weinstein domain $X$ necessarily admits Reeb chords. The existence of this Reeb chords either follows from an obstruction to the deformation of the boundary to a cylinder over a Legendrian sub-manifold or from the fact that the wrapped Floer homology of the Lagrangian vanishes once this boundary have been collared.
We study the combinatorial Reeb flow on the boundary of a four-dimensional convex polytope. We establish a correspondence between combinatorial Reeb orbits for a polytope, and ordinary Reeb orbits for a smoothing of the polytope, respecting action an
We show that a nondegenerate tight contact form on the 3-sphere has exactly two simple closed Reeb orbits if and only if the differential in linearized contact homology vanishes. Moreover, in this case the Floquet multipliers and Conley-Zehnder indic
Lagrangian cobordisms between Legendrian knots arise in Symplectic Field Theory and impose an interesting and not well-understood relation on Legendrian knots. There are some known elementary building blocks for Lagrangian cobordisms that are smoothl
Let k>2. We prove that the cotangent bundles of oriented homotopy (2k-1)-spheres S and S are symplectomorphic only if the classes defined by S and S agree up to sign in the quotient group of oriented homotopy spheres modulo those which bound parallel
We construct families of imaginary special Lagrangian cylinders near transverse Maslov index $0$ or $n$ intersection points of positive Lagrangian submanifolds in a general Calabi-Yau manifold. Hence, we obtain geodesics of open positive Lagrangian s