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Part i MONOPOLE CONSTRUCTION
28 other sections not shown
abelian Higgs model assume assumption asymptotic Banach space bounded Chapter compact completes the proof components configuration const convergent Corollary covariant derivative critical point curvature defined denote differential ensures equations 1.4 establish estimate exists a constant exponential decay fact finite action solution follows Furthermore gauge equivalent gauge group gauge transformation given Hence Higgs field Holder's inequality homotopy class identity implies inner product instantons invariant isomorphism LEMMA Lie algebra Lie group linear locally square integrable lower semicontinuous magnetic maximum principle monopole norm obtain open set particles principal G-bundle Proof Of Proposition proof of Theorem Proposition 7.5 prove real analytic Remark representation second order equations smooth connection smooth solution Sobolev inequality solitons solution to 1.4 solution to equations statement strictly convex sufficiently superconducting Suppose symmetric term Theorem 1.1 uniformly values variational equations vector bundle vortices Yang-Mills-Higgs equations zero