We describe the structure of minimal round functions on compact closed surfaces and three-dimensional manifolds. The minimal possible number of critical loops is determined and typical non-equisingular round function germs are interpreted in the spirit of isolated line singularities. We also discuss a version of Lusternik-Schnirelmann theory suitable for round functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-12,
author = {Georgi Khimshiashvili and Dirk Siersma},
title = {Remarks on minimal round functions},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {159-172},
zbl = {1063.57028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-12}
}
Georgi Khimshiashvili; Dirk Siersma. Remarks on minimal round functions. Banach Center Publications, Tome 60 (2003) pp. 159-172. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-12/