941 research outputs found
Bifurcation of periodic solutions to the singular Yamabe problem on spheres
We obtain uncountably many periodic solutions to the singular Yamabe problem
on a round sphere, that blow up along a great circle. These are (complete)
constant scalar curvature metrics on the complement of inside ,
, that are conformal to the round (incomplete) metric and "periodic"
in the sense of being invariant under a discrete group of conformal
transformations. These solutions come from bifurcating branches of constant
scalar curvature metrics on compact quotients of .Comment: LaTeX2e, 12 pages, final version. To appear in J. Differential Geo
Deforming solutions of geometric variational problems with varying symmetry groups
We prove an equivariant implicit function theorem for variational problems
that are invariant under a varying symmetry group (corresponding to a bundle of
Lie groups). Motivated by applications to families of geometric variational
problems lacking regularity, several non-smooth extensions of the result are
discussed. Among such applications is the submanifold problem of deforming the
ambient metric preserving a given variational property of a prescribed family
of submanifolds, e.g., constant mean curvature, up to the action of the
corresponding ambient isometry groups.Comment: LaTeX2e, 26 pages, to appear in Transform. Group
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