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math.DG2003
A remark on capillary surfaces in a 3-dimensional space of constant curvature
Alexander Arbieto, Carlos Matheus, Marcos Petrucio
We generalize a theorem by J. Choe on capillary surfaces for arbitrary 3-dimensional spaces of constant curvature. The main tools in this paper are an extension of a theorem of H.…
math.DG2003
Geometrical versus Topological Properties of Manifolds
Carlos Matheus, Krerley Oliveira
Given a compact -dimensional immersed Riemannian manifold in some Euclidean space we prove that if the Hausdorff dimension of the singular set of the Gauss map is small, t…
math.DG2003
Immersions with fractal set of points of zero Gauss-Kronecker curvature
Alexander Arbieto, Carlos Matheus
We construct, for any ``good'' Cantor set of , an immersion of the sphere with set of points of zero Gauss-Kronecker curvature equal to , where $D…