COMPACTNESS ON THE SPACE OF BOUNDED TRAJECTORIES IN SYMPLECTIC MANIFOLD

Abstract

Symplectic 다양체 내의 두 개의 Lagrangian 부분 다양체를 연결하는 smooth path 공간에 symplectic action의 gradient flow가 정의된다. 두번째 호모토피 군이 0일때, gradient flow가 유계인 괴적들의 공간상에서 Compactness 성질을 조사한다.;We consider the gradient flow of the symplectic action on the space of smooth paths which join two Lagrangian submanifolds of the symplectic manifold. We investigate compactness property for the set of bounded gradient trajectories on any compact set of the domain when the second homotopy group vanishes.