We study in this paper the scalar curvature equation on S². We give two explicit constructions of the scalar curvature functions by perturbing constant with suitable spherical harmonic polynomials. Multiplicity results for the corresponding scalar curvature equations are proved through the calculation of the topological degree of the associated map G for each scalar curvature functions. Copyright © 2019 Research India Publications.
|Journal||Advances in Theoretical and Applied Mathematics|
|Publication status||Published - 2019|
CitationCheung, K. L. (2019). Multiplicity results for the scalar curvature equation on S². Advances in Theoretical and Applied Mathematics, 14(1), 17-46.
- Scalar curvature equations
- Degree of maps
- Multiplicity of solutions