Minimal surfaces in a complex projective space whose mean curvature vectors are eigenvectors.
Minimal surfaces in foliated manifolds.
Minimal surfaces in pseudohermitian geometry
We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation...
Minimal surfaces in sub-riemannian manifolds and structure of their singular sets in the case
We study minimal surfaces in sub-riemannian manifolds with sub-riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail -dimensional surfaces in contact manifolds of dimension . We show that in this case minimal surfaces are projections of a special class of -dimensional surfaces...
Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the (2,3) case
We study minimal surfaces in sub-Riemannian manifolds with sub-Riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail 2-dimensional surfaces in contact manifolds of dimension 3. We show that in this case minimal surfaces are projections of a special class of 2-dimensional surfaces...
Minimal surfaces via loop groups.
Minimal Surfaces with Isolated Singularities.
Minimal tensor product immersions.
Minimal tori in S4.
Multiple convex hypersurfaces with prescribed mean curvature
(n-2)-tightness and curvature of submanifolds with boundary.
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.