Classification of fractional, singular Yamabe metrics on a twice punctured sphere I
Authors
João Henrique Andrade
Azahara DelaTorre
João Marcos do Ò
Jesse Ratzkin
Juncheng Wei
Abstract
The Delaunay metrics form a family of conformally flat, constant fractional Q-curvature metrics on a twice-punctured sphere. They are all (after a Möbius transformation) rotationally symmetric and periodic, and admit several elegant variational descriptions. We prove that, when s is close to but less than 1, any complete, conformally flat constant Q-curvature metric on a twice-punctured sphere is a Delaunay metric. Along the way, we prove a sharp a priori bound for the conformal factor of these metrics, which may be of independent interest.
