Maximum Principles for Null Hypersurfaces and Null Splitting Theorems
نویسندگان
چکیده
منابع مشابه
Maximum Principles for Null Hypersurfaces and Null Splitting Theorems
The geometric maximum principle for smooth (spacelike) hypersurfaces, which is a consequence of Alexandrov’s [1] strong maximum for second order quasilinear elliptic operators, is a basic tool in Riemannian and Lorentzian geometry. In [2], extending earlier work of Eschenburg [7], a version of the geometric maximum principle in the Lorentzian setting was obtained for rough (C) spacelike hypersu...
متن کاملMaximum Principle for Totally Umbilical Null Hypersurfaces and Time-dependent Null Horizons
In this paper we modify the maximum principal of (Galloway, 2000) for totally geodesic null hypersurfaces by proving a geometric maximum principle which obeys mean curvature inequalities of a family of totally umbilical null hypersurfaces of a spacetime manifold (Theorem 6). As a physical interpretation we show that, in particular, for a prescribed class of spacetimes the geometric inequality o...
متن کاملCompact null hypersurfaces and collapsing Riemannian manifolds
Restrictions are obtained on the topology of a compact divergence-free null hypersurface in a four-dimensional Lorentzian manifold whose Ricci tensor is zero or satisfies some weaker conditions. This is done by showing that each null hypersurface of this type can be used to construct a family of three-dimensional Riemannian metrics which collapses with bounded curvature and applying known resul...
متن کاملMapped Null Hypersurfaces and Legendrian Maps
For an (m+1)-dimensional space-time (X, g), define a mapped null hypersurface to be a smooth map ν : N → X (that is not necessarily an immersion) such that there exists a smooth field of null lines along ν that are both tangent and g-orthogonal to ν. We study relations between mapped null hypersurfaces and Legendrian maps to the spherical cotangent bundle ST M of an immersed spacelike hypersurf...
متن کاملSingularity analysis of pseudo null hypersurfaces and pseudo hyperbolic hypersurfaces
This paper introduces the notions of pseudo null curves in Minkowski 4-space. Meanwhile, some geometrical characterizations and the singularities of pseudo null hypersurfaces and pseudo hyperbolic hypersurfaces, which are generated by pseudo null curves, are considered in this paper. c ©2016 All rights reserved.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Henri Poincaré
سال: 2000
ISSN: 1424-0637
DOI: 10.1007/s000230050006