6 papers
Uncountably many non-rotationally symmetric type II ancient Yamabe flows on the sphere
Haixia Chen, Seunghyeok Kim, Monica Musso
For every , we construct uncountably many families of type II ancient solutions to the Yamabe flow on the unit round -sphere $\Ss^n$. These families are pairwise distin…
Compactness and non-compactness theorems of the fourth- and sixth-order constant -curvature problems
Liuwei Gong, Seunghyeok Kim, Juncheng Wei
We provide a complete resolution to the question of compactness for the full solution sets of the fourth-order and sixth-order constant -curvature problems on smooth closed Riem…
Sharp quantitative stability estimates for the Brezis-Nirenberg problem
Haixia Chen, Seunghyeok Kim, Juncheng Wei
We study the quantitative stability for the classical Brezis-Nirenberg problem associated with the critical Sobolev embedding in…
Weighted isoperimetric ratios and extension problems for fractional conformal Laplacians
Sangdon Jin, Seunghyeok Kim
We investigate a novel connection between the weighted isoperimetric problems and the weighted Poisson integrals of the extension problems for nonlocal elliptic operators. We first…
Sharp quantitative stability estimates for critical points of fractional Sobolev inequalities
Haixia Chen, Seunghyeok Kim, Juncheng Wei
By developing a unified approach based on integral representations, we establish sharp quantitative stability estimates for critical points of the fractional Sobolev inequalities i…
Sharp quantitative stability of the Yamabe problem
Haixia Chen, Seunghyeok Kim
Given a smooth closed Riemannian manifold of dimension , we derive sharp quantitative stability estimates for nonnegative functions near the solution set of the Ya…