The evolution of harmonic mappings with free boundaries.
The evolution of the scalar curvature of a surface to a prescribed function
We investigate the gradient flow associated to the prescribed scalar curvature problem on compact riemannian surfaces. We prove the global existence and the convergence at infinity of this flow under sufficient conditions on the prescribed function, which we suppose just continuous. In particular, this gives a uniform approach to solve the prescribed scalar curvature problem for general compact surfaces.
The Evolution of the Weyl Tensor under the Ricci Flow
We compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons.
The Existence of Embedded Minimal Surfaces and the Problem of Uniqueness.
The existence of negatively Ricci curved metrics on three manifolds.
The Existence of Polarized F-structure on Volume Collapsed 4-manifolds.
The existence problem of hyperbolic structures on vector bundles.
The explicit construction of all harmonic two-spheres in G2 (Rn).
The explicit construction of Einstein Finsler metrics with non-constant flag curvature.
The faces of the Grassmanian of three-planes in R7 (Calibrated geometries on R7).
The Family of Horospheres Through Two Points.
The family of isometric superconformal harmonic maps and the affine Toda equations.
The filling radius of homogeneous manifolds
The first eigenvalue of spacelike submanifolds in indefinite space form
In this paper, we prove that the first eigenvalue of a complete spacelike submanifold in with the bounded Gauss map must be zero.
The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold
The First Eigenvalue of the Laplacian of an Isoparametric Minimal Hypersurface in a Unit Sphere.
The first eigenvalue of the laplacian on manifolds of non-negative curvature
The Foliation of Semigroups by Congruence Classes.
The Free Loop Space of Globally Symmetric Spaces.
The Frölicher-Nijenhuis bracket on some functional spaces
Two fiber bundles E₁ and E₂ over the same base space M yield the fibered set ℱ(E₁,E₂) → M, whose fibers are defined as , for each x ∈ M. This fibered set can be regarded as a smooth space in the sense of Frölicher and we construct its tangent prolongation. Then we extend the Frölicher-Nijenhuis bracket to projectable tangent valued forms on ℱ(E₁,E₂). These forms turn out to be a kind of differential operators. In particular, we consider a general connection on ℱ(E₁,E₂) and study the associated...