A Characteristic Eigenfunction for Minimal Hypersurfaces in Space Forms.
A characterization of minimal surfaces in with parallel normal vector field.
A characterization of shortest geodesics on surfaces.
A Compactness Theorem for Surfaces with Lp-Bounded Second Fundamental Form.
A Convergence Theorem for Immersions with <>-Bounded Second Fundamental Form
A direct method approach for the existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature.
A general optimal inequality for arbitrary Riemannian submanifolds.
A generalization of Steiner Symmetrization for immersed surfaces and its applications.
A half-space type property in the Euclidean sphere
We study the notion of strong -stability for the context of closed hypersurfaces () with constant -th mean curvature immersed into the Euclidean sphere , where . In this setting, under a suitable restriction on the -th mean curvature , we establish that there are no -strongly stable closed hypersurfaces immersed in a certain region of , a region that is determined by a totally umbilical sphere of . We also provide a rigidity result for such hypersurfaces.
A lower bound for the i-th total absolute curvature of an immersion
A new characterization of -stable hypersurfaces in space forms
In this paper we study the -stability of closed hypersurfaces with constant -th mean curvature in Riemannian manifolds of constant sectional curvature. In this setting, we obtain a characterization of the -stable ones through of the analysis of the first eigenvalue of an operator naturally attached to the -th mean curvature.
A New Conformal Invariant and Its Applications to the Wilmore Conjecture and the First Eigenvalue of Compact Surfaces.
A new obstruction to minimal isometric immersions into a real space form.
A non-existence theorem for stable constant mena curvature hypersurfaces.
A non-immersion theorem for hyperbolic manifolds.
A note about the problem of conformal deformation of metrics in the unit ball.
A note on stability of minimal surfaces in -dimensional hyperbolic space .
A Note on Stability of Minimal Surfaces in n-dimensional Hyperbolic Space Hn(c)
A note on surfaces with prescribed oriented Euclidean Gauss map.
A note on the nonexistence of spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form
We obtain nonexistence results concerning complete noncompact spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form, under the assumption that the support functions with respect to a fixed nonzero vector are linearly related. Our approach is based on a suitable maximum principle recently established by Alías, Caminha and do Nascimento [3].