Ju n 20 16 A NON - EXISTENCE RESULT FOR MINIMAL CATENOIDS IN ASYMPTOTICALLY FLAT SPACES
نویسنده
چکیده
In General Relativity, asymptotically flat manifolds naturally arise as spacelike slices in space-times describing isolated gravitational systems. Due to their self-evident physical relevance, their geometry has been extensively studied and a variety of fundamental results have been obtained. Among these, the mean-curvature proof of the Positive Mass Theorem proposed by Schoen and Yau [SY79] has disclosed a fundamental principle, which basically asserts that an asymptotically Schwarzschildean manifold (of non-negative scalar curvature, as prescribed by the dominant energy condition) cannot contain an asymptotically planar stable minimal surface. In fact, much more recently, the following non-existence result has been obtained by the first-named author:
منابع مشابه
A non-existence result for minimal catenoids in asymptotically flat spaces
We show that asymptotically Schwarzschildean 3-manifolds cannot contain minimal surfaces obtained by perturbative deformations of a Euclidean catenoid, no matter how small the ADM mass of the ambient space and how large the neck of the catenoid itself. Such an obstruction is sharply three-dimensional and ceases to hold for more general classes of asymptotically flat data.
متن کاملLindelöf's Theorem for Catenoids Revisited
In this paper we study the maximal stable domains on minimal catenoids in Euclidean and hyperbolic spaces and in H2 × R. We in particular investigate whether half-vertical catenoids are maximal stable domains (Lindelöf’s property). We also consider stable domains on catenoid-cousins in hyperbolic space. Our motivations come from Lindelöf’s 1870 paper on catenoids in Euclidean space. Mathematics...
متن کاملGluing and Moduli for Noncompact Geometric Problems
The existence results we discuss for each of these problems are ones whereby known solutions (sometimes satisfying certain nondegeneracy hypotheses) are glued together to produce new solutions. Although this sort of procedure is quite well-known, there have been some recent advances on which we wish to report here. We also discuss what has been established about the moduli spaces of all solutio...
متن کاملFixed points for total asymptotically nonexpansive mappings in a new version of bead space
The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...
متن کامل