Bandwidth and focal radius with positive isotropic curvature
Tsz-Kiu Aaron Chow, Jingze Zhu
TL;DR
This paper establishes bounds on bandwidth and focal radius for hypersurfaces in manifolds with positive isotropic curvature, using spectral analysis of a twisted de Rham-Hodge operator, advancing geometric understanding of PIC manifolds.
Contribution
It provides new quantitative inequalities relating bandwidth and focal radius to boundary convexities and Betti numbers in PIC manifolds, employing spectral methods.
Findings
Upper bounds on bandwidth in PIC manifolds
Upper bounds on focal radius in PIC manifolds
Spectral properties of twisted de Rham-Hodge operator used
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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Taxonomy
TopicsOptical Imaging and Spectroscopy Techniques