[毕业论文] 三个带拓扑约束的变分问题 [复制链接]

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毕业论文-三个带拓扑约束的变分问题，共62页，

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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• 毕业论文-三个带拓扑约束的变分问题
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