On the

Yuxin Ge Universit´e Paris Est Cr´eteil Val de Marne Chang-Shou Lin National Taiwan University Guofang Wang Albert-Ludwigs-Universit¨at Freiburg

Differential Geometry mathscidoc:1609.10155

Journal of Differential Geometry, 84, (1), 45-86, 2010
In this paper, we establish an analytic foundation for a fully non-linear equation 2 1 = f on manifolds with metrics of positive scalar curvature and apply it to give a (rough) classification of such manifolds. A crucial point is a simple observation that this equation is a degenerate elliptic equation without any condition on the sign of f and it is elliptic not only for f > 0 but also for f < 0. By defining a Yamabe constant Y2,1 with respect to this equation, we show that a manifold with metrics of positive scalar curvature admits a conformal metric of positive scalar curvature and positive 2-scalar curvature if and only if Y2,1 > 0. We give a complete solution for the corresponding Yamabe problem. Namely, let g0 be a positive scalar curvature metric, then in its conformal class there is a conformal metric with 2(g) = 1(g), for some constant . Using these analytic results, we give a rough classification of the space of manifolds with metrics of positive scalar curvature.
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  title={ON THE },
  author={Yuxin Ge, Chang-Shou Lin, and Guofang Wang},
  booktitle={Journal of Differential Geometry},
Yuxin Ge, Chang-Shou Lin, and Guofang Wang. ON THE . 2010. Vol. 84. In Journal of Differential Geometry. pp.45-86. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911204745412475812.
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