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

TL;DR

This paper establishes a regularity result for conformal metrics with controlled scalar curvature and a lower bound on the first eigenvalue of the Laplacian, contributing to geometric analysis.

Contribution

It provides a new regularity theorem for conformal metrics with integral scalar curvature bounds and spectral constraints, extending previous results in geometric analysis.

Findings

Regularity of conformal metrics under scalar curvature bounds

Lower bounds on the first eigenvalue influence metric regularity

Extension of scalar curvature regularity results to new spectral conditions

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 $B > \Lambda_1(S^n,[g_{st.}]).$