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- W1985387978 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper M Superscript n Baseline comma g right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>M</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>g</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>({M^n},g)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a complete noncompact Riemannian manifold with the curvature bounded between two negative constants. Given a function <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper K> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=application/x-tex>K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M Superscript n> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>M</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{M^n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, in terms of the behaviors of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper K> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=application/x-tex>K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> at infinite, we give a fairly complete answer to when the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper K> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=application/x-tex>K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> can be the scalar curvature function of a complete metric <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=g 1> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>g</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{g_1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which is conformal to <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>." @default.
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- W1985387978 date "1993-01-01" @default.
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- W1985387978 title "Prescribing scalar curvatures on the conformal classes of complete metrics with negative curvature" @default.
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