Classification of fractional, singular Yamabe metrics on a twice punctured sphere I

Fuente: arXiv
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Main Authors: Andrade, João Henrique, DelaTorre, Azahara, Ò, João Marcos do, Ratzkin, Jesse, Wei, Juncheng
Format: Preprint
Published: 2025
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_version_ 1866914184522891264
author Andrade, João Henrique
DelaTorre, Azahara
Ò, João Marcos do
Ratzkin, Jesse
Wei, Juncheng
author_facet Andrade, João Henrique
DelaTorre, Azahara
Ò, João Marcos do
Ratzkin, Jesse
Wei, Juncheng
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_05225
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Classification of fractional, singular Yamabe metrics on a twice punctured sphere I
Andrade, João Henrique
DelaTorre, Azahara
Ò, João Marcos do
Ratzkin, Jesse
Wei, Juncheng
Differential Geometry
Analysis of PDEs
35J60, 35R11, 53C21, 53A30, 35B33, 35B40
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.
title Classification of fractional, singular Yamabe metrics on a twice punctured sphere I
topic Differential Geometry
Analysis of PDEs
35J60, 35R11, 53C21, 53A30, 35B33, 35B40
url https://arxiv.org/abs/2511.05225