2 problems

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The pair-of-ends conjecture for orientable locally conformally flat ALE manifolds
Let $n\geq 5$ , and let $(M,g)$ be an orientable, locally conformally flat ALE manifold with nonnegative scalar curvature. A non-trivial ALE end is an ALE end that is not the standa…
Conjectureopenale-manifolds conformal-geometry orbifoldsarXiv posted 2 days ago
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Non-existence conjecture for Hermitian non-Kähler ALE gravitational instantons
Non-existence conjecture. There exist no Hermitian non-Kähler ALE gravitational instantons, without any restrictions on the structure group, except for the Eguchi–Hanson metric wit…
Conjectureopenale-manifolds complex-geometry ricci-flat-geometryarXiv posted 2 days ago

The pair-of-ends conjecture for orientable locally conformally flat ALE manifolds