Free Boundary Minimal Annuli in Convex Three-manifolds
نویسنده
چکیده
We prove the existence of free boundary minimal annuli inside suitably convex subsets of three-dimensional Riemannian manifolds with nonnegative Ricci curvature − including strictly convex domains of the Euclidean space R.
منابع مشابه
Compactness of the Space of Embedded Minimal Surfaces with Free Boundary in Three-manifolds with Nonnegative Ricci Curvature and Convex Boundary
We prove a lower bound for the first Steklov eigenvalue of embedded minimal hypersurfaces with free boundary in a compact n-dimensional Riemannian manifold which has nonnegative Ricci curvature and strictly convex boundary. When n “ 3, this implies an apriori curvature estimate for these minimal surfaces in terms of the geometry of the ambient manifold and the topology of the minimal surface. A...
متن کاملMetrics with Non-negative Ricci Curvature on Convex Three-manifolds
We prove that the space of smooth Riemannian metrics on the three-ball with non-negative Ricci curvature and strictly convex boundary is path-connected; and, moreover, that the associated moduli space (i.e., modulo orientation-preserving diffeomorphisms of the threeball) is contractible. As an application, using results of Maximo, Nunes, and Smith [MNS], we show the existence of properly embedd...
متن کاملThe Space of Minimal Annuli Bounded by an Extremal Pair of Planar Curves
In 1956 Shiffman [14] proved that every minimally immersed annulus in 3 bounded by convex curves in parallel planes is embedded. He proved this theorem by showing that the minimal annulus was foliated by convex curves in parallel planes. We are able to prove a related embeddedness theorem for extremal convex planar curves. Recall that a subset of 3 is extremal if it is contained on the boundary...
متن کاملMinimal Surfaces Bounded by a Pair of Convex Planar Curves
In 1956 M. Shiffman [9] proved several beautiful theorems concerning the geometry of a minimal annulus A whose boundary consists of two closed smooth convex curves in parallel planes P{, P2. The first theorem stated that the intersection of A with any plane P, between P{ and P2, is a convex Jordan curve. In particular it follows that A is embedded. He then used this convexity theorem to prove t...
متن کاملMinimal Surfaces Bounded by Convex Curves in Parallel Planes
In 1956 M. Shiffman [17] proved several beautiful theorems concerning the geometry of a minimal annulus A whose boundary consists of two closed convex curves in parallel planes P1, P2. The first theorem stated that the intersection of A with any plane P , between P1 and P2, is a convex Jordan curve. In particular it follows that A is embedded. He then used this convexity theorem to prove that e...
متن کامل