A corrected quantitative version of the Morse lemma
S\'ebastien Gou\"ezel, Vladimir Shchur
TL;DR
This paper corrects a gap in the proof of a key theorem regarding optimal bounds in the Morse lemma for Gromov-hyperbolic spaces and provides a computer-verified certification of the corrected result.
Contribution
It identifies and fixes a proof gap in a previous work and offers a computer-verified certification of the corrected theorem.
Findings
The main theorem in [ShCh13a] is now confirmed as correct.
A computer certification process validates the corrected proof.
The correction ensures the reliability of bounds in Gromov-hyperbolic spaces.
Abstract
There is a gap in the proof of the main theorem in the article [ShCh13a] on optimal bounds for the Morse lemma in Gromov-hyperbolic spaces. We correct this gap, showing that the main theorem of [ShCh13a] is correct. We also describe a computer certification of this result.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows