The quantitative Morse theorem
Ta Le Loi, Phan Phien
TL;DR
This paper provides a proof of the quantitative Morse theorem, utilizing quantitative versions of Sard's theorem, the inverse function theorem, and the Morse lemma to establish precise bounds.
Contribution
It offers a rigorous proof of the quantitative Morse theorem based on quantitative analytical tools, advancing the understanding of Morse theory with explicit estimates.
Findings
Proof of the quantitative Morse theorem established
Utilizes quantitative Sard, inverse function, and Morse lemmas
Provides explicit bounds and estimates in Morse theory
Abstract
In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Topological and Geometric Data Analysis · Mathematical Analysis and Transform Methods