Boundary operators associated to the σ k -curvature

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We study conformal deformation problems on manifolds with boundary which include prescribing σ k ≡0 in the interior. In particular, we prove a Dirichlet principle when the induced metric on the boundary is fixed and an Obata-type theorem on the upper hemisphere. We introduce some conformally covariant multilinear operators as a key technical tool.

Original languageEnglish (US)
Pages (from-to)83-106
Number of pages24
JournalAdvances in Mathematics
StatePublished - Oct 15 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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