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An almost-almost-Schur lemma on the 3-sphere
Tobias König, Jonas W. Peteranderl
In the conformal class of the standard metric on the -sphere, we prove a quantitative refinement of the Andrews-De Lellis-Topping inequality in terms of a two-term distance to t…
Sharp quantitative integral inequalities for harmonic extensions
Rupert L. Frank, Jonas W. Peteranderl, Larry Read
We prove a quantitative version of a sharp integral inequality by Hang, Wang, and Yan for both the Poisson operator and its adjoint. Our result has the strongest possible norm and…
The sharp -curvature inequality on the sphere in quantitative form
Rupert L. Frank, Jonas W. Peteranderl
Among all metrics on with that are conformal to the standard metric and have positive scalar curvature, the total -curvature, normalized by the volume, is…
Degenerate Stability of the Caffarelli-Kohn-Nirenberg Inequality along the Felli-Schneider Curve
Rupert L. Frank, Jonas W. Peteranderl
We show that the Caffarelli-Kohn-Nirenberg (CKN) inequality holds with a remainder term that is quartic in the distance to the set of optimizers for the full parameter range of the…