Hypersurfaces of finite geometric type
by
Francesco Mercuri
Universidade Estadual de Campinas, Unicamp, Brazil
Coauthors: J.L. Marques Barbosa, R. Fukuoka

Oral Communication

We introduce, based on the properties of complete minimal surfaces of finite total curvature, a new class of hypersurfaces of Euclidean spaces, the hypersurfaces of finite geometric type, which is a much wider class, even in dimension two. First we extend to this class some results known for complete minimal surfaces of finite total curvature, as for example, the fact that the Gauss map omits at most three points. Second we use those ideas to study higher dimensional situations, which includes, strictly, the minimal hypersurfaces regular at infinity introduced by Shoen. For example we give a characterization of even dimensional cathenoids as the minimal hypersurfaces, regular at infinity, whoseGauss-Kroneker curvature is zero only on "low dimensional subsets".

Date received: June 13, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafh-20.