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Hyperbolic Multi-Monopoles With Arbitrary Mass
On a complete manifold, such as Euclidean 3-space or hyperbolic 3-space, the
limit at infinity of the norm of the Higgs field is called the mass of the
monopole. We show the existence, on hypebolic 3-space, of monopoles with given
magnetic charge and arbitrary mass. Previously, aside from charge one
monopoles, existence was known only for monopoles with integral mass (since
these arise from U(1) invariant instantons on Euclidean 4-space). The method of
proof is based on Taubes' gluing procedure, using well-separated, explicit,
charge one monopoles. The analysis is carried out in a weighted Sobolev space
and necessitates eliminating the possibility of point spectra.Comment: 20 page