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- W2482307565 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper M comma g right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo>,</mml:mo> <mml:mi>g</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(M,g)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a compact Riemannian manifold of dimension <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n greater-than-or-equal-to 3> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n geq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. A well-known conjecture states that the set of constant scalar curvature metrics in the conformal class of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=g> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding=application/x-tex>g</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is compact unless <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper M comma g right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo>,</mml:mo> <mml:mi>g</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(M,g)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is conformally equivalent to the round sphere. In this paper, we construct counterexamples to this conjecture in dimensions <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n greater-than-or-equal-to 52> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>52</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n geq 52</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
- W2482307565 created "2016-08-23" @default.
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- W2482307565 date "2007-06-14" @default.
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- W2482307565 title "Blow-up phenomena for the Yamabe equation" @default.
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- W2482307565 doi "https://doi.org/10.1090/s0894-0347-07-00575-9" @default.
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