On a compact cylinder X×I with positive scalar curvature and nonnegative mean curvature, the angle condition guarantees existence of a metric with positive scalar curvature on X, forcing negative mean curvature if X admits none.
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Scalar and Mean Curvature Comparison on Compact Cylinder
On a compact cylinder X×I with positive scalar curvature and nonnegative mean curvature, the angle condition guarantees existence of a metric with positive scalar curvature on X, forcing negative mean curvature if X admits none.