Caustic of the three-dimensional ellipsoid. (Caustique de la surface ellipsoïdale à trois dimensions.)
Characterizations of conformally flat hypersurfaces
Compact Hypersurfaces with a Constant Higher Mean Curvature Function.
Compact hypersurfaces with constant higher order mean curvatures.
A fundamental question about hypersurfaces in the Euclidean space is to decide if the sphere is the only compact hypersurface (embedded or immersed) with constant higher order mean curvature Hr, for some r = 1, ..., n.
Complete real Kähler Euclidean hypersurfaces are cylinders
In this note we show that any complete Kähler (immersed) Euclidean hypersurface must be the product of a surface in with an Euclidean factor .
Conditions on the projective curvature tensor of hypersurfaces in euclidian space
Constant mean curvature surfaces in -space forms
Construction of compact constant mean curvature hypersurfaces with topology
In this paper, we explain how the end-to-end construction together with the moduli space theory can be used to produce compact constant mean curvature hypersurfaces with nontrivial topology. For the sake of simplicity, the hypersurfaces we construct have a large group of symmetry but the method can certainly be used to provide many more examples with less symmetries.
Courbures et basculements des sous-variétés riemanniennes
Curvature and torsion formulas for conflict sets
Conflict set are the points at equal distance from a number of manifolds. Known results on the differential geometry of these sets are generalized and extended.
Cylindrically Taut Immersions.