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- W2077321063 abstract "In this short article, we interpret the condition of a theorem of Gursky-Viaclovsky concerning the nonnegativity of the Paneitz operator as the metric being <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=3> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=application/x-tex>3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-positive Ricci. By a result of Wolfson, this condition can be preserved under the surgery of codimension <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=q greater-than-or-equal-to 3> <mml:semantics> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>qgeq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Combining these two observations, we expand the list of manifolds which admit metrics with a nonnegative Paneitz operator. Consequently, there exist metrics of constant <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Q> <mml:semantics> <mml:mi>Q</mml:mi> <mml:annotation encoding=application/x-tex>Q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-curvature on these manifolds." @default.
- W2077321063 created "2016-06-24" @default.
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- W2077321063 date "2015-04-01" @default.
- W2077321063 modified "2023-09-27" @default.
- W2077321063 title "A remark on the nonnegativity of the Paneitz operator" @default.
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- W2077321063 doi "https://doi.org/10.1090/s0002-9939-2015-12604-4" @default.
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