2006/09/07 by Michael Greenblatt, Greenblatt, Michael
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.math/0609217
openalex publication_date 2006/09/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, a geometric resolution of singularities algorithm is developed. This method is elementary in its statement and proof, using explicit coordinate systems as much as possible. Each coordinate change used in the resolution procedure is one-to-one on its domain, and is of one of a few explicit canonical forms. As applications of these methods to classical analysis, two theorems are proven. First and foremost, a general theorem regarding the existence of critical integrability exponents is established. Secondly, a new proof of a well-known inequality of Lojasiewicz is given.