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arXiv · 2603.07021

The local Morse Homology of the critical points in the Lagrange problem

Xiuting Tang
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Abstract

In this paper, we construct local Morse homology in a new way and compute the local Morse homology of the critical points of the Lagrange problem. As a corollary, we prove for the first time that each of the linear critical points is either a saddle point or a degenerate critical point compared to the previous conclusion that if all the linear critical points are non-degenerate, they are saddle points.

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Xiuting Tang. 2026-03-07. The local Morse Homology of the critical points in the Lagrange problem. https://arxiv.org/abs/2603.07021

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