ELEVEN DIMENSION SUPERGRAVITY EQUATIONS ON EDGE MANIFOLDS
XUWEN ZHU
Abstract
We consider the eleven dimensional supergravity equations on edge manifolds, which is a system
of nonlinear equations on the product manifold B7 × S4 . We compute the indicial roots of the
linearized equations and construct a real-valued generalized inverse using the edge calculus and the
scattering matrix on hyperbolic space. Then we use the implicit function theorem to prove that all
the solutions are prescribed by three pairs of data on the boundary sphere.
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