Bandwidth and focal radius with positive isotropic curvature

Published 30 May 2024 in math.DG and math.GT | (2405.20129v1)

Abstract: This paper investigates quantitative metric inequalities for manifolds with positive isotropic curvature (PIC). Our results include upper bounds on the bandwidth and focal radius of hypersurfaces in PIC manifolds, contingent on boundary convexities and Betti numbers. The proof is based on exploiting the spectral properties of a twisted de Rham-Hodge operator on manifolds with boundary.

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