【摘要】
We present an explicit representation formula of Green function for the general GJMS operator on the round sphere in various cases, including fractional GJMS operator, critical and noncritical dimension etc. Our approach emphasizes the importance of Gegenbauer polynomials, and can be applied to related topics. Next, we raise a conjecture about a spherical rigidity of Green function for GJMS operator on a hypersurface in Euclidean space. Especially, we are able to prove weak rigidity for GJMS operator of order two and four, meanwhile providing some evidences to support the strong rigidity conjecture. Some natural questions remain open. This is jointly with Yalong Shi.
