A remark on minimal surfaces with circles with normal curvature of constant radius

Regular minimal nets on surfaces of constant negative curvature

The problem of classification of closed local minimal nets on surfaces of constant negative curvature has been formulated in [3], [4] in the context of the famous Plateau problem in the one-dimensional case. In [6] an asymptotic for log ♯(W (g)) as g → +∞ where g is genus and W (g) is the set of regular single-face closed local minimal nets on surfaces of curvature −1 has been obtained. It has ...

A Remark on Kähler Metrics of Constant Scalar Curvature on Ruled Complex Surfaces

In this note we point out how some recent developments in the theory of constant scalar curvature Kähler metrics can be used to clarify the existence issue for such metrics in the special case of (geometrically) ruled complex surfaces. Dedicated to Professor Paul Gauduchon on his 60th birthday.

A remark on capillary surfaces in a 3-dimensional space of constant curvature

We generalize a theorem by J. Choe on capillary surfaces for arbitrary 3-dimensional spaces of constant curvature. The main tools in this paper are an extension of a theorem of H. Hopf due to S.-S. Chern and two index lemmas by J. Choe.

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Constant mean curvature surfaces with boundary on a sphere

In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the boundary is prescribed or that the surface meets the sphere with a constant angle. We study under what geometric conditions the surface must be spherical. Our results apply in many scenarios in physics where in absence...