Boundary operators associated to the σk-curvature

Jeffrey S. Case; Yi Wang

doi:10.1016/j.aim.2018.08.004

Boundary operators associated to the σ_k-curvature

Jeffrey S. Case
, Yi Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	83-106
Number of pages	24
Journal	Advances in Mathematics
Volume	337
DOIs	https://doi.org/10.1016/j.aim.2018.08.004
State	Published - Oct 15 2018

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.aim.2018.08.004

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title = "Boundary operators associated to the σk-curvature",

abstract = "We study conformal deformation problems on manifolds with boundary which include prescribing σk≡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.",

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T1 - Boundary operators associated to the σk-curvature

AU - Case, Jeffrey S.

AU - Wang, Yi

PY - 2018/10/15

Y1 - 2018/10/15

N2 - We study conformal deformation problems on manifolds with boundary which include prescribing σk≡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.

AB - We study conformal deformation problems on manifolds with boundary which include prescribing σk≡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.

UR - https://www.scopus.com/pages/publications/85052616646

UR - https://www.scopus.com/pages/publications/85052616646#tab=citedBy

U2 - 10.1016/j.aim.2018.08.004

DO - 10.1016/j.aim.2018.08.004

M3 - Article

AN - SCOPUS:85052616646

SN - 0001-8708

VL - 337

SP - 83

EP - 106

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Boundary operators associated to the σ_k-curvature

Abstract

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