Prescribing symmetric scalar curvature onS
2 |
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Authors: | Min Ji |
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Institution: | (1) Graduate School, University of Science and Technology of China, 100039 Bajing, China |
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Abstract: | The problem of prescribing scalar curvature in S2 is discussed, and the solvability of the equation-Δu + 2 - Reu = 0on S2,is given, where R ∈ C0 (S2).It is known that there are some obstructions. Some new results are given by seeking a solution of the minimax type. For example,
supposing that R is Gsymmetric and is constant on the set of fixed points on S2
under G (where Gis a subgroup of O(3)), itis proved that the equation is solvable if and only if Ris positive somewhere. |
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Keywords: | scalar curvature critical point symmetric function minimax solution transformation group |
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