The classical Minkowski inequality in the Euclidean space provides a lower bound on total mean curvature of hypersurface terms surface area, which is optimal round spheres. In this paper we employ locally constrained inverse flow to prove properly defined analogue Lorentzian de Sitter space.

The novel STEVE (i.e., Space-Time-Enclosing Volume Extraction) algorithm is described here for the very first time. It generates iso-valued hypersurfaces that may be implicitly contained in four-dimensional (4D) data sets, such as temporal sequences of three-dimensional images from time-varying computed tomography. Any final hypersurface that will be generated by STEVE is guaranteed to be free ...

We consider a brane N = I × S0, where S0 is an ndimensional space form, not necessarily compact, in a SchwarzschildAdS(n+2) bulk N and prove that, for specific negative pressures on the brane, the brane is an ARW space. By reflecting N and N to N̂ and N̂ , the joint branes N ∪ N̂ can be naturally embedded as a C∞hypersurface in R2 ×S0, if n is odd and if ω = − n−1 2 is chosen, a value that corresp...

This paper concerns the evolution of a closed hypersurface dimension [Formula: see text] in Euclidean space under mixed volume preserving flow. The speed equals power homogeneous curvature functions degree one and either convex or concave plus term, including case powers mean Gauss curvature. main result is that if initial satisfies suitable pinching condition, there exists unique, smooth solut...

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...

We study the number of flux vacua for type IIB string theory on an orientifold of the Calabi-Yau expressed as a hypersurface in WCP 4 [1, 1, 2, 2, 6] by evaluating a suitable integral over the complex-structure moduli space as per the conjecture of Douglas and Ashok. We show that away from the singular conifold locus, one gets a power law, and that the (neighborhood) of the conifold locus indee...

Einstein hypersurfaces are “very rare” in rank-one symmetric spaces. Damek-Ricci spaces may be viewed as the closest and most natural generalisations of noncompact We prove that no space admits an hypersurface.

Consider a smooth manifold with a smooth metric which changes bilinear type from Riemann to Lorentz on a hypersurface Σ with radical tangent to Σ. Two natural bilinear symmetric forms appear there, and we use it to analyze the geometry of Σ. We show the way in which these forms control the smooth extensibility over Σ of the covariant, sectional and Ricci curvatures of the Levi-Civita connection...