On the local isometric imbedding problem of 2-dimensional Riemannian manifolds in Euclidean space
On the maximal spacelike submanifolds of a pseudo-Riemannian quasi constant curvature manifold.
On the maximum principle for principal curvatures
The paper contains the estimates from above of the principal curvatures of the solution to some curvature equations. A correction of the author's previous argument is presented.
On the Mean Curvature of R-Spaces.
On the moduli space of superminimal surfaces in spheres.
On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture
Let M̅ be a compact Riemannian manifold with sectional curvature satisfying (resp. ), which can be isometrically immersed as a hypersurface in the Euclidean space (resp. the unit Euclidean sphere). Then there exist no stable compact minimal submanifolds in M̅. This extends Shen and Xu’s result for 1/4-pinched Riemannian manifolds and also suggests a modified version of the well-known Lawson-Simons conjecture.
On the nullity index of isometric immersions of Kähler manifolds
On the number of minimal two-spheres of small area in manifolds with curvature bounded above.
On the problem whether the image of a given differentiable map into Riemannian manifold is contained in a submanifold with parallel second fundamental form.
On the quadric CMC spacelike hypersurfaces in Lorentzian space forms
We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.
On the Simon Conjecture for Minimal Immersions with S1-symmetry.
On the structure of convex sets with applications to the moduli of spherical minimal immersions.
On the twistor bundle of de Sitter space .
On the type decomposition of the second fundamental form of a Kähler submanifold
On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces, I.
On the volume of unit vector fields on a compact semisimple Lie group.
On Tight Immersions of Maximal Codimension.
On total curvature of immersions and minimal submanifolds of spheres
For closed immersed submanifolds of Euclidean spaces, we prove that , where is the mean curvature field, the volume of the given submanifold and is the radius of the smallest sphere enclosing the submanifold. Moreover, we prove that the equality holds only for minimal submanifolds of this sphere.
On totally real minimal submanifolds in complex projective space
In this paper, we obtain some pinching theorems for totally real minimal submanifolds in complex projective space.
On totally real submanifolds in a nearly Kähler manifold.