A quantitative obstruction to collapsing surfaces
Mikhail G. Katz
TL;DR
This paper introduces a quantitative criterion that prevents certain high-genus surfaces from collapsing under specific curvature and diameter constraints, advancing understanding in geometric topology.
Contribution
It presents a novel quantitative obstruction to surface collapsing, linking curvature, diameter, and other geometric invariants.
Findings
Establishes a new obstruction criterion for surface collapse.
Connects curvature, diameter, and volume in the context of surface topology.
Provides bounds related to Gromov-Hausdorff distance and systole.
Abstract
We provide a quantitative obstruction to collapsing surfaces of genus at least 2 under a lower curvature bound and an upper diameter bound. Keywords: curvature; diameter; volume; filling radius; systole; Gromov-Hausdorff distance
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