Green functions for GJMS operators on spheres, Gegenbauer polynomials and rigidity theorems
arxiv(2024)
摘要
We derive explicit representation formulae of Green functions for GJMS
operators on n-spheres, including the fractional ones. These formulae not
only have natural geometric interpretations concerning the extrinsic geometry
of the round sphere, but also reflect the spherical rigidity among closed
embedded hypersurfaces in ℝ^n+1.
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