Reducing smooth functions to normal forms near critical points

2022/06/01 by Orevkova, A. S.
#37C15 #58K05 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.00628

Abstract

The paper is devoted to "uniform" reduction of smooth functions on 2-manifolds to canonical form near critical points by some coordinate changes in some neighbourhoods of these points. For singularity types E₆,E₈ and A_n, we explicitly construct such coordinate changes and estimate from below (in terms of C^r-norm of the function) the radius of a required neighbourhood.

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