Multiplicity results for the scalar curvature equation on S²

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Abstract

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.
Original languageEnglish
Pages (from-to)17-46
JournalAdvances in Theoretical and Applied Mathematics
Volume14
Issue number1
Publication statusPublished - 2019

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Multiplicity Results
Scalar Curvature
Harmonic Polynomials
Topological Degree
Spherical Harmonics

Citation

Cheung, K. L. (2019). Multiplicity results for the scalar curvature equation on S². Advances in Theoretical and Applied Mathematics, 14(1), 17-46.

Keywords

  • Scalar curvature equations
  • Degree of maps
  • Multiplicity of solutions