Ask a Question

Prefer a chat interface with context about you and your work?

Smoothing $L^\infty$ Riemannian metrics with nonnegative scalar curvature outside of a singular set

Smoothing $L^\infty$ Riemannian metrics with nonnegative scalar curvature outside of a singular set

We show that any $L^\infty$ Riemannian metric $g$ on $\mathbb{R}^n$ that is smooth with nonnegative scalar curvature away from a singular set of finite $(n-\alpha)$-dimensional Minkowski content, for some $\alpha>2$, admits an approximation by smooth Riemannian metrics with nonnegative scalar curvature, provided that $g$ is sufficiently close in $L^\infty$ to …