A'Campo curvature bumps and the Dirac phenomenon near a singular point
Algebraic Geometry
2017-05-17 v3 Differential Geometry
Abstract
The level curves of an analytic function germ almost always have bumps at unexpected points near the singularity. This profound discovery of N. A'Campo is fully explored in this paper for , using the Newton-Puiseux infinitesimals and the notion of gradient canyon. Equally unexpected is the Dirac phenomenon: as , the total Gaussian curvature of accumulates in the gradient canyons.
Keywords
Cite
@article{arxiv.1206.0525,
title = {A'Campo curvature bumps and the Dirac phenomenon near a singular point},
author = {S. Koike and T-C. Kuo and L. Paunescu},
journal= {arXiv preprint arXiv:1206.0525},
year = {2017}
}