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

6 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

Mathematics(all)

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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.",

author = "Case, {Jeffrey S.} and Yi Wang",

note = "Funding Information: YW was partially supported by NSF Grant No. DMS-1612015. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

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doi = "10.1016/j.aim.2018.08.004",

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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.

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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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