A fourth-order Cherrier-Escobar problem with prescribed corner behavior on the half-ball

Abstract

Click on the DOI link to access this article at the publishers website (may not be free).We show that the half-ball in $R _4$ can be conformally changed so that the only contribution to the Gauss-Bonnet formula is a constant term at the corner. This may be seen as a fourth-order Cherrier-Escobar-type problem on the half-ball.Funding text 1 This work was initiated and significantly advanced during the workshop Partial differential equations and conformal geometry held at the American Institute of Mathematics (AIM) in August 2022. We thank AIM for providing an ideal research environment. We are grateful for helpful conversations with Matthew Gursky, Tzu-Mo Kuo, and Andrew Waldron. The referee read carefully and made valuable suggestions. JSC was partially supported by a grant from the Simons Foundation (Grant No. 524601). Y-J.L. was partially supported by a grant from the National Science Foundation (Grant No. DMS-2418740). SEM was partially supported by a grant from the Simons Foundation (Grant No. 966614). CBN was partially supported by a grant from the National Science Foundation (Grant No. DMS-2000164). PY was partially supported by a grant from the National Science Foundation (Grant No. DMS-1509505). Funding text 2 JSC was partially supported by a grant from the Simons Foundation (Grant No. 524601 ). Y-J.L. was partially supported by a grant from the National Science Foundation (Grant No. DMS-2418740 ). SEM was partially supported by a grant from the Simons Foundation (Grant No. 966614 ). CBN was partially supported by a grant from the National Science Foundation (Grant No. DMS-2000164 ). PY was partially supported by a grant from the National Science Foundation (Grant No. DMS-1509505 )