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Research Report MRR01-021
Monotonicity Formulae and Curvature Equations
John Urbas
Abstract:
We derive local integral estimates and monotonicity
formulae for certain curvature quantities related to hypersurfaces
of prescribed k-th mean curvature. We use these to improve
interior curvature bounds established in previous work, and to
derive a local Hölder gradient estimate for admissible
solutions of the equation of prescribed scalar curvature.
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