ﻻ يوجد ملخص باللغة العربية
Given a hypersurface $M$ of null scalar curvature in the unit sphere $mathbb{S}^n$, $nge 4$, such that its second fundamental form has rank greater than 2, we construct a singular scalar-flat hypersurface in $Rr^{n+1}$ as a normal graph over a truncated cone generated by $M$. Furthermore, this graph is 1-stable if the cone is strictly 1-stable.
A diagonal metric sum_{i=1}^n g_{ii} dx_i^2 is termed Guichard_k if sum_{i=1}^{n-k}g_{ii}-sum_{i=n-k+1}^n g_{ii}=0. A hypersurface in R^{n+1} is isothermic_k if it admits line of curvature co-ordinates such that its induced metric is Guichard_k. Isot
In this paper, we study biharmonic hypersurfaces in a product of an Einstein space and a real line. We prove that a biharmonic hypersurface with constant mean curvature in such a product is either minimal or a vertical cylinder generalizing a result
As is well known, self-similar solutions to the mean curvature flow, including self-shrinkers, translating solitons and self-expanders, arise naturally in the singularity analysis of the mean curvature flow. Recently, Guo cite{Guo} proved that $n$-di
We prove a theorem of Hadamard-Stoker type: a connected locally convex complete hypersurface immersed in $H^n times R$ (n>1), where $H^n$ is n-dimensional hyperbolic space, is embedded and homeomorphic either to the n-sphere or to $R^n$. In the latte
In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space $mathbb{R}^{n+1}_{