Scalar curvatures on 𝑆²

Chen, Wen Xiong; Ding, Wei Yue

doi:10.1090/S0002-9947-1987-0896027-4

Scalar curvatures on $S^ 2$
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by Wen Xiong Chen and Wei Yue Ding PDF

Trans. Amer. Math. Soc. 303 (1987), 365-382 Request permission

Abstract:

A theorem for the existence of solutions of the nonlinear elliptic equation $- \Delta u + 2 = R(x){e^u},\;x \in {S^2}$, is proved by using a "mass center" analysis technique and by applying a continuous "flow" in ${H^1}({S^2})$ controlled by $\nabla R$.

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A problem concerning the scalar curvature on

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