Multiple Point Blowup Phenomenon in Scalar Curvature Equations on Spheres of Dimension Greater Than Three
Let (S n,g o) be the standard n—sphere. The following question was raised by L. Nirenberg. Which function K on S2 is the Gauss curvature of a metric g on S 2 conformally equivalent to g o? Naturally one may ask a similar question in higher dimensional case, namely, which function K on S n is the scalar curvature of a metric g on Sn conformally equivalent to g o?
KeywordsScalar Curvature Morse Index Morse Function Constant Scalar Curvature High Dimensional Case
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