Regularity of conformal metrics with large first eigenvalue

Matthiesen, Henrik

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 5, pp. 1079-1094.

On démontre un résultat sur la régularité de métriques conformes de volumes unitaires avec une borne supérieure sur la norme $L^p$ de la courbure scalaire pour $p>n/2$, et une borne inférieure sur la première valeur propre de $\Delta$ par une constante $B>{\Lambda }_1(S^n,\left[g_{st.}\right]).$

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

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