On Conical Asymptotically Flat Manifolds (Journal of Mathematical Study, 2025)
We prove a conjecture of Petrunin and Tuschmann on the non-existence ofasymptotically flat 4-manifolds asymptotic to the half plane. We also survey recentprogress and questions concerning gravitational instantons, which serve as our motivation for studying this question.
Keywords: Asymptotically flat; collapsing; gravitational instanton.