Curve-straightening and the Palais-Smale condition
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چکیده
منابع مشابه
Curve-straightening and the Palais-smale Condition
This paper considers the negative gradient trajectories associated with the modified total squared curvature functional ∫ k2 + ν ds. The focus is on the limiting behavior as ν tends to zero from the positive side. It is shown that when ν = 0 spaces of curves exist in which some trajectories converge and others diverge. In one instance the collection of critical points splits into two subsets. A...
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We prove that for a uniformly convex Lagrangian system L on a compact manifold M , almost all energy levels contain a periodic orbit. We also prove that below Mañé’s critical value of the lift of the Lagrangian to the universal cover, cu(L), almost all energy levels have conjugate points. We prove that if the energy level [E = k] is of contact type and M 6= T then the free time action functiona...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1998
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-98-01977-1