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].
A parametrization of the Weierstrass formulae and perturbation of complete minimal surfaces in R3 into the hyperbolic 3-space.
A perturbation result concerning a second solution to the Dirichlet problem for the equation of prescribed mean curvature.
A pinching theorem on complete submanifolds with parallel mean curvature vectors
Let M be an n-dimensional complete immersed submanifold with parallel mean curvature vectors in an (n+p)-dimensional Riemannian manifold N of constant curvature c > 0. Denote the square of length and the length of the trace of the second fundamental tensor of M by S and H, respectively. We prove that if S ≤ 1/(n-1) H² + 2c, n ≥ 4, or S ≤ 1/2 H² + min(2,(3p-3)/(2p-3))c, n = 3, then M is umbilical. This result generalizes the Okumura-Hasanis...
A projective Gauss map associated with a hypersurface and a hyperplane.
A rigidity theorem for Riemann's minimal surfaces
We describe first the analytic structure of Riemann’s examples of singly-periodic minimal surfaces; we also characterize them as extensions of minimal annuli bounded by parallel straight lines between parallel planes. We then prove their uniqueness as solutions of the perturbed problem of a punctured annulus, and we present standard methods for determining finite total curvature periodic minimal surfaces and solving the period problems.
A series of Kählerian invariants and their applications to Kählerian geometry.
A Weierstrass-Kenmotsu formula for prescribed mean curvature surfaces in hyperbolic space
Affine maximal hypersurfaces
This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss affine Bernstein problems and complete constant mean curvature surfaces in equiaffine differential geometry.
Algebraic representation formulas for null curves in Sl(2,ℂ)
We study curves in Sl(2,ℂ) whose tangent vectors have vanishing length with respect to the biinvariant conformal metric induced by the Killing form, so-called null curves. We establish differential invariants of them that resemble infinitesimal arc length, curvature and torsion of ordinary curves in Euclidean 3-space. We discuss various differential-algebraic representation formulas for null curves. One of them, a modification of the Bianchi-Small formula, gives an Sl(2,ℂ)-equivariant bijection...
An estimate of the pinching constant of minimal hypersurfaces with constant scalar curvature in the unit sphere.
An existence result for minimal spheres in manifolds boundary
We prove the existence of a not homotopically trivial minimal sphere in a 3-manifold with boundary, obtained by deleting an open connected subset from a compact Riemannian oriented 3-manifold with boundary, having trivial second homotopy group.
An extension of a result of H. Hopf to Kähler submanifolds of
An Extrinsic Rigity Theorem for Minimal Surfaces in S3.
An Inequality between the Exterior Diameter and the Mean Curvature of Bounded Immersions.
An integral formula for Willmore surfaces in an -dimensional sphere.
Analytic extension of a maximal surface in along its boundary.
Anwendungen der differentialtopologischen Berechnung der totalen Krümmung und totalen Absolutkrümmung in der sphärischen Differentialgeometrie.