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On positive scalar curvature on S 2

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Abstract.

We consider the problem of prescribing scalar curvature on the standard 2-sphere S 2. It is proved that any positive smooth function on S 2 is the scalar curvature of some pointwise conformal metric, if an associated map has non-zero degree. As a result we improve some previous important results and give some completely new ones.

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Authors and Affiliations

  1. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, Beijing, China

    Min Ji

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  1. Min Ji
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Correspondence to Min Ji.

Additional information

Received: 21 January 2003, Accepted: 12 March 2003, Published online: 6 June 2003

Mathematics Subject Classification (2000):

35J60, 58G03

Min Ji: Supported in part by the NSF grant 19725102 and the 973 grant G1999075107 of China

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Ji, M. On positive scalar curvature on S 2 . Cal Var 19, 165–182 (2004). https://doi.org/10.1007/s00526-003-0214-0

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  • DOI: https://doi.org/10.1007/s00526-003-0214-0

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