Universal bounds for eigenvalues of Schrödinger operators on Riemannian manifolds.
Harmonic maps and the topology of manifolds with positive spectrum and stable minimal hypersurfaces.
In this paper, we prove two Liouville theorems for harmonic maps and apply them to study the topology of manifolds with positive spectrum and stable minimal hypersurfaces in Riemannian manifolds with non-negative bi-Ricci curvature.
Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space
In this paper we study the topological and metric rigidity of hypersurfaces in , the -dimensional hyperbolic space of sectional curvature . We find conditions to ensure a complete connected oriented hypersurface in to be diffeomorphic to a Euclidean sphere. We also give sufficient conditions for a complete connected oriented closed hypersurface with constant norm of the second fundamental form to be totally umbilic.
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