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畢業論文 三個帶拓撲約束的變分問題

  • 簡介:畢業論文-三個帶拓撲約束的變分問題,共62頁,,In this article we briefly review some important functionals in modern physics,by the language of differential geometry: Chern-Simons functional, Ginzburg-Landau,functi...
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適用專業:數學與應用數學
適用年級:大學
論文編號:209541

論文簡介:
畢業論文-三個帶拓撲約束的變分問題,共62頁,
In this article we briefly review some important functionals in modern physics
by the language of differential geometry: Chern-Simons functional, Ginzburg-Landau
functional and static knot energy. We present some properties of the solutions to the
corresponding Euler-Lagrange equations obtained from the variation of the functionals.
After that we calculate Chern-Simons functional on some 3-manifolds (e.g., Berger
sphere, warped product 3-manifolds) which obtain particular features in physics. We
also try to generalize the potential term in Ginzburg-Landau functional and get a reduced
form of this functional, involving the Chern class, on conformal Riemannian
manifolds. Finally we generalize the static knot energy in Faddeev model and get an
estimate between the Faddeev energy and the Hopf invariant, basing on which the existence
of the solution to the minimization problem can be proved.


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  • 畢業論文-三個帶拓撲約束的變分問題
  • pdf畢業論文-三個帶拓撲約束的變分問題.pdf  [4.98MB]

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