Constant mean curvature surfaces in Sol with non-empty boundary
نویسنده
چکیده
In homogenous space Sol we study compact surfaces with constant mean curvature and with non-empty boundary. We ask how the geometry of the boundary curve imposes restrictions over all possible configurations that the surface can adopt. We obtain a flux formula and we establish results that assert that, under some restrictions, the symmetry of the boundary is inherited into the surface. MSC: 53A10
منابع مشابه
Hyperbolic surfaces of $L_1$-2-type
In this paper, we show that an $L_1$-2-type surface in the three-dimensional hyperbolic space $H^3subset R^4_1$ either is an open piece of a standard Riemannian product $ H^1(-sqrt{1+r^2})times S^{1}(r)$, or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.
متن کاملInvariant surfaces in homogenous space Sol with constant curvature
A surface in homogenous space Sol is said to be an invariant surface if it is invariant under some of the two 1-parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces. In this work we study invariant surfaces that satisfy a certain condition on their curvatures. We classify invariant surfaces with constant mean curvature and constant Gaussian curv...
متن کاملA ug 2 00 6 AREA - STATIONARY SURFACES INSIDE THE SUB - RIEMANNIAN THREE - SPHERE
We consider the sub-Riemannian metric g h on S 3 provided by the restriction of the Riemannian metric of curvature 1 to the plane distribution orthogonal to the Hopf vector field. We compute the geodesics associated to the Carnot-Carathéodory distance and we show that, depending on their curvature, they are closed or dense subsets of a Clifford torus. We study area-stationary surfaces with or w...
متن کاملSurfaces with maximal constant mean curvature
In this note we consider asymptotically flat manifolds with non-negative scalar curvature and an inner boundary which is an outermost minimal surface. We show that there exists an upper bound on the mean curvature of a constant mean curvature surface homologous to a subset of the interior boundary components. This bound allows us to find a maximizer for the constant mean curvature of a surface ...
متن کاملSurfaces of Constant Mean Curvature Bounded by Two Planar Curves ? RAFAEL LÓPEZ
In this paper we study constant mean curvature compact surfaces with two Jordan curves in parallel planes as boundary and we investigate the point at which the surface inherits the symmetries of its boundary.
متن کامل