Related papers: The Weinstein conjecture in the uniruled manifolds

A symplectic manifold $(M,\omega)$ is called {\em (symplectically) uniruled} if there is a nonzero genus zero GW invariant involving a point constraint. We prove that symplectic uniruledness is invariant under symplectic blow-up and…

We prove some Liouville type theorems on smooth compact Riemannian manifolds with nonnegative sectional curvature and strictly convex boundary. This gives a nonlinear generalization in low dimension of the recent sharp lower bound of the…

The conjectures of Manin and Peyre are confirmed for a certain threefold.

Weinstein trisection is a trisection of a symplectic 4-manifold whose 1-handlebodies are the Weinstein domain for the symplectic structure induced from an ambient manifold. Lambert-Cole, Meier, and Starkston showed that every closed…

A Liouville-type result for the p-Laplacian on complete Riemannian manifolds is proved. As an application are present some results concerning complete non-compact hypersurfaces immersed in a suitable warped product manifold.

We generalize Witten's conjectured formula relating Donaldson and Seiberg-Witten invariants to manifolds of non-simple type, via equivariant localization techniques. This approach does not use the theory of non-abelian monopoles, but works…

A conjecture expressing genus 1 Gromov-Witten invariants in mirror-theoretic terms of semi-simple Frobenius structures and complex oscillating integrals is formulated. The proof of the conjecture is given for torus-equivariant Gromov -…

In this paper, we establish a general relationship between the nonvanishing of GW invariants with the existence of the closed orbits of a Hamiltonian system. As an application, we completely solved the stabilized Weinstein conjecture.

We obtain some Liouville type theorems for positive harmonic functions on compact Riemannian manifolds with nonnegative Ricci curvature and strictly convex boundary and partially verifies Wang's conjecture (J. Geom. Anal. 31 (2021)). For…

Let $(M,\omega)$ be a symplectic manifold endowed with a agrangian foliation ${\cal L}$, it has been shown by Weinstein [16] hat the symplectic structure of $M$ defines on each leaf of ${\cal L}$, connection which curvature and torsion…

The existence of a "Plastikstufe" for a contact structure implies the Weinstein conjecture for all supporting contact forms.

We prove a normal form theorem for Poisson structures around Poisson transversals (also called cosymplectic submanifolds), which simultaneously generalizes Weinstein's symplectic neighborhood theorem from symplectic geometry and Weinstein's…

We extend the Marsden-Weinstein reduction theorem and the Darboux-Moser-Weinstein theorem to symplectic Lie algebroids. We also obtain a coisotropic embedding theorem for symplectic Lie algebroids.

In this paper we determine conditions of existence of an induced Riemannian structure on the symplectic quotient of a symplectic and Riemannian manifold following the action of a Lie group acting upon it in a hamiltonian way with…

We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.

We prove the Weinstein conjecture for non-trivial contact connected sums under either of two topological conditions: non-trivial fundamental group or torsion-free homology.

In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of $b$-symplectic manifolds started in [12], we prove a slice theorem for Lie group actions on $b$-symplectic manifolds.

In this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of $b^m$-symplectic manifolds. Novel techniques are introduced to associate smooth symplectic forms to the…

We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.

We study certain typical semilinear elliptic equations in Euclidean space $\bR^{n}$ or on a closed manifold $M$ with nonnegative Ricci curvature. Our proof is based on a crucial integral identity constructed by the invariant tensor method.…