5 papers
Stability for the Affine Sobolev Inequality and its Critical Points for
Rupert L. Frank, Yinqin Li, Dachun Yang
We prove stability for the affine Sobolev inequality for exponents with best possible norm and best possible stability exponent. We also show a corresponding result for c…
From Bogoliubov-de Gennes to Ginzburg-Landau: Critical Points Near in the Non-Magnetic Case
Rupert L. Frank, Christian Hainzl, Dong Hao Ou Yang
We study the relation between the Bogoliubov-de Gennes (BdG) equation and the Ginzburg-Landau (GL) equation for a BCS model without external fields. While previous rigorous derivat…
Jost solutions and direct scattering for the continuum Calogero-Moser equation
Rupert L. Frank, Larry Read
We propose an inverse scattering transform for the continuum Calogero-Moser equation. We give a rigorous treatment of the direct scattering problem by constructing the associated J…
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…