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라그라지안 휘트니트릭과 넓이조건

Title
라그라지안 휘트니트릭과 넓이조건
Other Titles
The Lagrangian Whitney Trick and The Area Condition
Author
김주희
Alternative Author(s)
Kim, Ju-Hee
Advisor(s)
변양현
Issue Date
2007-08
Publisher
한양대학교
Degree
Master
Abstract
Let D be an open disk in R² and consider the open subset D×R^(n-1)×R^(n-1) of R^(2n) with the standard symplectic structure. Also let l_(0), l₁be two open arcs in D which are closed as subsets of D meeting each other transversely at exactly two points. We construct a Hamiltonian flow with compact support, Ψ_(u) : D×R^(n-1)×R^(n-1)→D×R^(n-1)×R^(n-1), 0 ≤ u ≤ 1 such that Ψ_(0) = 1 and . Ψ₁(l_(0)×R^(n-1)×0)∩(l₁×0×R^(n-1)) = φ. Construction of such Ψ_(u), 0 ≤ u ≤ 1, deserves called a Lagrangian Whitney trick. We will show that the condition is needed involving the areas of the regions D in divided by l_(0) and l₁for the construction.
URI
https://repository.hanyang.ac.kr/handle/20.500.11754/148950http://hanyang.dcollection.net/common/orgView/200000407189
Appears in Collections:
GRADUATE SCHOOL[S](대학원) > MATHEMATICS(수학과) > Theses (Master)
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