The author first proves the existences of J-holomorphic curves in the symplectizations of Legendre fibrations and then as an application confirms the Weinstein conjectures on contact manifolds of Legendre fibrations. ...The author first proves the existences of J-holomorphic curves in the symplectizations of Legendre fibrations and then as an application confirms the Weinstein conjectures on contact manifolds of Legendre fibrations. As a corollary a new proof on the theorem due to Hofer,Viterbo, Gluck, Ziller, Weinstein and Ljusternik-Fet Theorem is provided, which is quite different from their original proofs.展开更多
In this paper, using pseudo-holomorphic curve method, one proves the Weinstein conjecture in the product P;×P;of two strongly geometrically bounded symplectic manifolds under some conditions with P;. In particula...In this paper, using pseudo-holomorphic curve method, one proves the Weinstein conjecture in the product P;×P;of two strongly geometrically bounded symplectic manifolds under some conditions with P;. In particular, if N is a closed manifold or a noncompact manifold of finite topological type, our result implies that the Weinstein conjecture in CP;×T*N holds.展开更多
This paper proves that on any tamed closed almost complex four-manifold(M,J)whose dimension of J-anti-invariant cohomology is equal to the self-dual second Betti number minus one,there exists a new symplectic form com...This paper proves that on any tamed closed almost complex four-manifold(M,J)whose dimension of J-anti-invariant cohomology is equal to the self-dual second Betti number minus one,there exists a new symplectic form compatible with the given almost complex structure J.In particular,if the self-dual second Betti number is one,we give an affirmative answer to a question of Donaldson for tamed closed almost complex four-manifolds.Our approach is along the lines used by Buchdahl to give a unified proof of the Kodaira conjecture.展开更多
In this paper,we will prove that Floer homology equipped with either the intrinsic or exterior product is isomorphic to quantum homology as a ring.We will also prove that GW-invariants in Floer homology and quantum ho...In this paper,we will prove that Floer homology equipped with either the intrinsic or exterior product is isomorphic to quantum homology as a ring.We will also prove that GW-invariants in Floer homology and quantum homology are equivalent.展开更多
In this note, we prove that the symplectic blow-up or blow-down in the dimension 4 is rigid, i.e. the symplectic area of the divisor does not exceed the symplectic radius of the neighbourhood on which we do the blow-u...In this note, we prove that the symplectic blow-up or blow-down in the dimension 4 is rigid, i.e. the symplectic area of the divisor does not exceed the symplectic radius of the neighbourhood on which we do the blow-up or blow-down.展开更多
文摘The author first proves the existences of J-holomorphic curves in the symplectizations of Legendre fibrations and then as an application confirms the Weinstein conjectures on contact manifolds of Legendre fibrations. As a corollary a new proof on the theorem due to Hofer,Viterbo, Gluck, Ziller, Weinstein and Ljusternik-Fet Theorem is provided, which is quite different from their original proofs.
文摘In this paper, using pseudo-holomorphic curve method, one proves the Weinstein conjecture in the product P;×P;of two strongly geometrically bounded symplectic manifolds under some conditions with P;. In particular, if N is a closed manifold or a noncompact manifold of finite topological type, our result implies that the Weinstein conjecture in CP;×T*N holds.
基金supported by PRC Grant NSFC 11701226(Tan),11371309,11771377(Wang),11426195(Zhou),11471145(Zhu)Natural Science Foundation of Jiangsu Province BK20170519(Tan)+1 种基金University Science Research Project of Jiangsu Province 15KJB110024(Zhou)Foundation of Yangzhou University 2015CXJ003(Zhou).
文摘This paper proves that on any tamed closed almost complex four-manifold(M,J)whose dimension of J-anti-invariant cohomology is equal to the self-dual second Betti number minus one,there exists a new symplectic form compatible with the given almost complex structure J.In particular,if the self-dual second Betti number is one,we give an affirmative answer to a question of Donaldson for tamed closed almost complex four-manifolds.Our approach is along the lines used by Buchdahl to give a unified proof of the Kodaira conjecture.
文摘In this paper,we will prove that Floer homology equipped with either the intrinsic or exterior product is isomorphic to quantum homology as a ring.We will also prove that GW-invariants in Floer homology and quantum homology are equivalent.
基金Supported in part by the NSF of P. R. China the Foundation of Chinese Educational Committee for Returned Scholars.
文摘In this note, we prove that the symplectic blow-up or blow-down in the dimension 4 is rigid, i.e. the symplectic area of the divisor does not exceed the symplectic radius of the neighbourhood on which we do the blow-up or blow-down.
