Publication Date:
2015-09-03
Description:
The level curves of an analytic function germ can have bumps (maxima of Gaussian curvature) at unexpected points near the singularity. This phenomenon is fully explored for $f(z,w)\in {\mathbb {C}}\{z,w\}$ , using the Newton–Puiseux infinitesimals and the notion of gradient canyon. Equally unexpected is the Dirac phenomenon: as $c \rightarrow 0$ , the total Gaussian curvature of $f=c$ accumulates in the minimal gradient canyons, and nowhere else. Our approach mimics the introduction of polar coordinates in Analytic Geometry .
Print ISSN:
0024-6115
Electronic ISSN:
1460-244X
Topics:
Mathematics
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