Asymptotics of the Poisson kernel and Green's functions of the fractional conformal Laplacian
M Mayer, CB Ndiaye�- arXiv preprint arXiv:2107.11743, 2021 - arxiv.org
M Mayer, CB Ndiaye
arXiv preprint arXiv:2107.11743, 2021•arxiv.orgWe study the asymptotics of the Poisson kernel and Green's functions of the fractional
conformal Laplacian for conformal infinities of asymptotically hyperbolic manifolds. We
derive sharp expansions of the Poisson kernel and Green's functions of the conformal
Laplacian near their singularities. Our expansions of the Green's functions answer the first
part of the conjecture of Kim-Musso-Wei [22] in the case of locally flat conformal infinities of
Poincar\'e-Einstein manifolds and together with the Poisson kernel asymptotic is used also�…
conformal Laplacian for conformal infinities of asymptotically hyperbolic manifolds. We
derive sharp expansions of the Poisson kernel and Green's functions of the conformal
Laplacian near their singularities. Our expansions of the Green's functions answer the first
part of the conjecture of Kim-Musso-Wei [22] in the case of locally flat conformal infinities of
Poincar\'e-Einstein manifolds and together with the Poisson kernel asymptotic is used also�…
We study the asymptotics of the Poisson kernel and Green's functions of the fractional conformal Laplacian for conformal infinities of asymptotically hyperbolic manifolds. We derive sharp expansions of the Poisson kernel and Green's functions of the conformal Laplacian near their singularities. Our expansions of the Green's functions answer the first part of the conjecture of Kim-Musso-Wei[22] in the case of locally flat conformal infinities of Poincar\'e-Einstein manifolds and together with the Poisson kernel asymptotic is used also in our paper [25] to show solvability of the fractional Yamabe problem in that case. Our asymptotics of the Green's functions on the general case of conformal infinities of asymptotically hyperbolic space is used also in [30] to show solvability of the fractional Yamabe problem for conformal infinities of dimension and fractional parameter in to a global case left by previous works.
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