Isoparametric Hypersurfaces with Four or Six Distinct Principal Curvatures. Necessary Conditions on the Multiplicities.
Isoparametric hypersurfaces with less than four principal curvatures in a sphere
We characterize Clifford hypersurfaces and Cartan minimal hypersurfaces in a sphere by some properties of extrinsic shapes of their geodesics.
Isoparametric triple systems of FKM-Type II.
Isoperimetric inequalities for parametric variational problems
Isoperimetric inequalities on minimal submanifolds of space forms.
Isoperimetric problems on the sphere and on surfaces with density.
Killing graphs with prescribed mean curvature and riemannian submersions
k-Symmetric Submanifolds of RN.
harmonic -form on submanifold with weighted Poincaré inequality
We deal with complete submanifolds with weighted Poincaré inequality. By assuming the submanifold is -stable or has sufficiently small total curvature, we establish two vanishing theorems for harmonic -forms, which are extensions of the results of Dung-Seo and Cavalcante-Mirandola-Vitório.
Least Area Incompressible Surfaces in 3-Manifolds.
Legendrian dual surfaces in hyperbolic 3-space
We consider surfaces in hyperbolic 3-space and their duals. We study flat dual surfaces in hyperbolic 3-space by using extended Legendrian dualities between pseudo-hyperspheres in Lorentz-Minkowski 4-space. We define the flatness of a surface in hyperbolic 3-space by the degeneracy of its dual, which is similar to the case of the Gauss map of a surface in Euclidean 3-space. Such surfaces are a kind of ruled surfaces. Moreover, we investigate the singularities of these surfaces and the dualities...
Lignes de divergence pour les graphes à courbure moyenne constante
Locally symmetric immersions
We use reflections with respect to submanifolds and related geometric results to develop, inspired by the work of Ferus and other authors, in a unified way a local theory of extrinsic symmetric immersions and submanifolds in a general analytic Riemannian manifold and in locally symmetric spaces. In particular we treat the case of real and complex space forms and study additional relations with holomorphic and symplectic reflections when the ambient space is almost Hermitian. The global case is also...
Manifolds of Dimension 3 with Prescribed Positive Curvature and with Nontrivial Homology.
Maximum principle for hypersurfaces.
Maximum principles and nonexistence results for minimal submanifolds.
Maximum Principles for Minimal surfaces in R3 Having noncompact boundary and a uniqueness theorem for the helicoid.
Mean curvature comparison for tubular hypersurfaces in symmetric spaces.
Minimal anti-kahler holomorphic hypersurfaces
Minimal cones and the spherical Bernstein problem, II.