A regularity result for conformal metrics with large first eigenvalue and integral scalar curvature bounds

Abstract

We prove a regularity result for unit volume conformal metrics with integral scalar curvature bounds for $p>n/2$ and first eigenvalue of $\Delta$ bounded from below by a constant $B>{\Lambda }_1(S^n,[g_{st.}]).$

arXiv comment13 pages, improved presentation, details added, corrected statements for the application on isospectral metrics, to appear in Annales de la Faculté des Sciences de Toulouse