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math.DG2026

Geometric Rigidity via Almost-Harmonic Twisted Spinors

Francesco Bei, Simone Cecchini

We establish sharp scalar-curvature bounds and rigidity consequences of Gromov's exact-lift two-form method. Let ((M^n,g)), (n\geq 4) even, be a closed spin Riemannian manifold car…

math.DG2026

Stable -systoles, scalar curvature and spin comass bounds

Simone Cecchini, Sven Hirsch, Rudolf Zeidler

We prove a sharp stable -systolic inequality for complex projective space under the scalar curvature lower bound of the normalized Fubini-Study metric. If is diffeomorphic t…

math.DG2026

Rigidity of spin fill-ins with non-negative scalar curvature

Simone Cecchini, Sven Hirsch, Rudolf Zeidler

We establish new mean curvature rigidity theorems for spin fill-ins with non-negative scalar curvature using two different spinorial techniques. Our results address two questions b…

math.DG2025

Positive scalar curvature with point singularities

Simone Cecchini, Georg Frenck, Rudolf Zeidler

We show that in every dimension , there exists a smooth closed manifold which does not admit a smooth positive scalar curvature ("psc") metric, but admits an $\…