Nejsymetričtější variety
Neumann and second boundary value problems for hessian and Gauß curvature flows
New characterizations of linear Weingarten hypersurfaces immersed in the hyperbolic space
In this paper, we deal with complete linear Weingarten hypersurfaces immersed in the hyperbolic space , that is, complete hypersurfaces of whose mean curvature and normalized scalar curvature satisfy for some , . In this setting, under appropriate restrictions on the mean curvature and on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of . Furthermore, a rigidity result...
New examples of biharmonic maps in spheres
We give some new methods to construct nonharmonic biharmonic maps in the unit n-dimensional sphere 𝕊ⁿ.
New Examples of imbedded spherical soap bubbles in SN (1).
New examples of minimal Lagrangian tori in the complex projective plane.
New stability results for spheres and Wulff shapes
We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the -sense is -close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [Ro1] and [Ro].
Newton transformations on null hypersurfaces
Any rigged null hypersurface is provided with two shape operators: with respect to the rigging and the rigged vector fields respectively. The present paper deals with the Newton transformations built on both of them and establishes related curvature properties. The laters are used to derive necessary and sufficient conditions for higher-order umbilicity and maximality we introduced in passing, and develop general Minkowski-type formulas for the null hypersurface, supported by some physical models...
Nonnegativity for the Curvature Operator and Isotropy for Isometric Immersions.
Non-rational minimal spheres and minimizing cones.
Normally flat semiparallel submanifolds in space forms as immersed semisymmetric Riemannian manifolds
By means of the bundle of orthonormal frames adapted to the submanifold as in the title an explicit exposition is given for these submanifolds. Two theorems give a full description of the semisymmetric Riemannian manifolds which can be immersed as such submanifolds. A conjecture is verified for this case that among manifolds of conullity two only the planar type (in the sense of Kowalski) is possible.