On the Weinstein conjecture in higher dimensions
نویسندگان
چکیده
منابع مشابه
On the Weinstein Conjecture in Higher Dimensions
The first break-through on this conjecture was obtained by C. Viterbo, [19], showing that compact energy surfaces in R2n of contact-type have periodic orbits. Extending Gromov’s theory of pseudoholomorphic curves, [3], to symplectized contact manifolds, H. Hofer, [4], related the Weinstein conjecture to the existence of certain pseudoholomorphic curves. He showed that in dimension three the Wei...
متن کاملA Note On Weinstein Conjecture
In this article, we give new proofs on the some cases on Weinstein conjecture and get some new results on Weinstein conjecture.
متن کاملPseudo-holomorphic Curves and the Weinstein Conjecture
Let S ⊂ (N,ω) be a hypersurface in a symplectic manifold. The characteristic distribution LS on S consists of the tangent vectors v ∈ TS such that i(v)ωS = 0, where ωS is the pull back of ω to S. The flow lines generated by a vector field in LS are called characteristics. S ⊂ (N,ω) is said to be of contact type if there is a 1-form α on S such that dα = ωS and α(v) 6= 0 for any v 6= 0 in LS. Th...
متن کاملThe Weinstein conjecture for stable Hamiltonian structures
We use the equivalence between embedded contact homology and Seiberg-Witten Floer homology to obtain the following improvements on the Weinstein conjecture. Let Y be a closed oriented connected 3-manifold with a stable Hamiltonian structure, and let R denote the associated Reeb vector field on Y . We prove that if Y is not a T2 -bundle over S1 , then R has a closed orbit. Along the way we prove...
متن کاملFuglede's Conjecture Is False in 12 and Higher Dimensions
We give an example of a set Ω ⊂ R 12 which is a finite union of unit cubes, such that L 2 (Ω) admits an orthonormal basis of exponentials { 1 |Ω| 1/2 e 2πiξ j ·x : ξ j ∈ Λ} for some discrete set Λ ⊂ R 12 , but which does not tile R 12 by translations. This answers (one direction of) a conjecture of Fuglede [1] in the negative, at least in 12 and higher dimensions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2009
ISSN: 0010-2571
DOI: 10.4171/cmh/167