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Hamiltonian dynamics and symplectic 2-capacities | | Alvaro Pelayo
; San Vu Ngoc
; | | Date: |
4 Oct 2012 | | Abstract: | We show that the cylinder B^2(1) imes mathbb{R}^{2(n-1)}, n >= 3, may be
symplectically embedded into B^4(R) imes mathbb{R}^{2(n-2)} when R >=
sqrt{3}. This answers a question posed by H. Hofer in 1989. The existence of
such embeddings implies that there are no symplectic 2-capacities. We draw
essentially on the work of Guth, Hind, Kerman, and Polterovich, which shows
that B^2(1) imes B^{2(n-1)}(r) may be symplectically embedded into B^4(R)
imes mathbb{R}^{2(n-2)} for any finite r > 0 and R > sqrt{3}. We supply the
final arguments to answer Hofer’s question. The main tool is a construction to
remove singular limits of smooth families of embeddings. The construction can
also be used to answer a question of R. Hind and E. Kerman concerning
symplectic embeddings into products of the form B^2(R_1) imes B^2(R_2) imes
mathbb{R}^{2(n-2)}. | | Source: | arXiv, 1210.1537 | | Services: | Forum | Review | PDF | Favorites | |
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