arXiv subjects

Chun-gen Liu

Publications and source records attributed to Chun-gen Liu.

2 recordsLinked to original sources

arXiv2003

Cup-length estimate for Lagrangian intersections

In this paper we consider the Arnold conjecture on the Lagrangian intersections of some closed Lagrangian submanifold of a closed symplectic manifold with its image of a Hamiltonian diffeomorphism. We prove that if the Hofer's symplectic energy of the Hamiltonian diffeomorphism is less than a topology number defined by the Lagrangian submanifold, then the Arnold conjecture is true in the degenerated (non-transversal) case.

math.SG↗

arXiv2001

Multiplicity of closed characteristics on symmetric convex hypersurfaces in $\R^{2n}$

Let $Σ$ be a compact $C^2$ hypersurface in $\R^{2n}$ bounding a convex set with non-empty interior. In this paper it is proved that there always exist at least $n$ geometrically distinct closed characteristics on $Σ$ if $Σ$ is symmetric with respect to the origin.

math.DS↗