Title

Level Sets of Functions and Symmetry Sets of Surface Sections

Authors

André Diatta, University of Liverpool, UK
Peter Giblin, University of Liverpool, UK
Brendan Guilfoyle, Institute of Technology, Tralee, IrelandFollow
Wilhelm Klingenberg, University of Durham, UK

ORCID

0000-0002-7437-5046

Document Type

Conference Object

Disciplines

Mathematics | Physical Sciences and Mathematics

Publication Details

Lecture Notes in Computer Science, vol 3604. © 2005 Springer-Verlag Berlin Heidelberg

Abstract

We prove that the level sets of a real C s function of two variables near a non-degenerate critical point are of class C [s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at an elliptic or hyperbolic point, and in particular at an umbilic point. We go on to use the results to study symmetry sets of the planar sections. We also analyse one of the cases coming from a degenerate critical point, corresponding to an elliptic cusp of Gauss on a surface, where the differentiability is reduced to C [s/4]. However in all our applications we assume C  ∞  smoothness.

Recommended Citation

Diatta, A., Giblin, P., Guilfoyle, B., Klingenberg, W. (2005). Level Sets of Functions and Symmetry Sets of Surface Sections. In: Martin, R., Bez, H., Sabin, M. (eds) Mathematics of Surfaces XI. Lecture Notes in Computer Science, vol 3604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537908_9