Gradient Flow in Morse and Analytic Settings

2023/11/16 by Leyang Zhang, Zhang, Leyang
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2311.09968

openalex publication_date 2023/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This report is actually the in-class project of MATH489 FA2022, Dynamics and Differential Equations in University of Illinois Urbana-Champaign. The report is mainly about gradient flow of a Morse-type functions (Morse functions, Morse--Bott functions, etc.) and analytic functions. Several small results that I develop during the reading are included as well. They have a focus on the convergence, limiting rate and direction of gradient flow in either setting.

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