Resolves most remaining open cases for scalar-flat conformal metrics with prescribed boundary mean curvature via local test function construction and new solvability conditions.
Escobar, Sharp constant in a Sobolev trace inequality , Indiana Univ
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For T not equal to the Escobar threshold, the squared gradient norm minus Φ(T)^2 is bounded below by α_T times the squared distance to the minimizer set plus a higher-order term, for all functions in the constraint set A_T.
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Conformal Scalar-Flat Metrics with Prescribed Boundary Mean Curvature
Resolves most remaining open cases for scalar-flat conformal metrics with prescribed boundary mean curvature via local test function construction and new solvability conditions.
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A note on the Sobolev--Escobar bridge inequality
For T not equal to the Escobar threshold, the squared gradient norm minus Φ(T)^2 is bounded below by α_T times the squared distance to the minimizer set plus a higher-order term, for all functions in the constraint set A_T.