Volume growth and puncture repair in conformal geometry

Abstract

Suppose $M$ is a compact Riemannian manifold and $p\in M$ an arbitrary point. We employ estimates on the volume growth around $p$ to prove that the only conformal compactification of $M\setminus \{p\}$ is $M$ itself.

7 pages

Cited by in corpus (2)

• Modular forms, projective structures, and the four squares theorem
• Puncture repair on metric measure spaces