arXiv subjects

Levi Lopes de Lima

Publications and source records attributed to Levi Lopes de Lima.

38 records · Page 3Linked to original sources

arXiv2001

CMC-1 Surfaces in Hyperbolic 3-space using the Bianchi-Calo method

In this note we present a method for constructing CMC-1 surfaces in hyperbolic 3-space $\bfH^3(-1)$ in terms of holomorphic data first introduced in Bianchi's Lezioni di Geometria Differenziale of 1927, therefore predating by many years the modern approaches due to Bryant, Small and others. Besides its obvious historical interest, this note aims to complement Bianchi's analysis by deriving explicit formulae for CMC-1 surfaces and comparing the various approaches encountered in the literature.

math.DG↗

arXiv2000

Index Growth of hypersurfaces with constant mean curvature

In this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature (cmc) 1 in $\R^{n}$ (Delaunay unduloids). When $n=3$, using the asymptotics result of Korevaar, Kusner and Solomon, we derive an explicit asymptotic index growth rate for finite topology cmc 1 surfaces with properly embedded ends. Similar results are obtained for hypersurfaces with cmc bigger than 1 in hyperbolic space.

math.DG↗