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The research aims to establish the flatness of certain metrics on closed manifolds with isolated singularities under nonnegative scalar curvature.

Singular Metrics with Nonnegative Scalar Curvature and RCD

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The research aims to establish the flatness of certain metrics on closed manifolds with isolated singularities under nonnegative scalar curvature.
Investigation of uniformly Euclidean metrics with isolated singularities on closed manifolds.
Analysis of nonnegative synthetic Ricci curvature as a critical proof technique.
Consideration of singular sets composed of finite unions of submanifolds.
Proved that metrics with nonnegative scalar curvature are flat and smoothly extend over singularities.
Confirmed Schoen’s Conjecture for specific closed manifolds with isolated singularities.
Provided conditions under which the results hold for various intersecting submanifolds.

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Demonstrates the flatness of Euclidean metrics with singularities, confirming Schoen’s Conjecture in specified cases.

Dai et al. (2026) studied this question.

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