ﻻ يوجد ملخص باللغة العربية
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 latter case it is either a vertical graph over a convex domain in $H^n$ or has what we call a simple end.
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
We give lower bounds for the fundamental tone of open sets in submanifolds with locally bounded mean curvature in $ N times mathbb{R}$, where $N$ is an $n$-dimensional complete Riemannian manifold with radial sectional curvature $K_{N} leq kappa$. Wh
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 trunca
In [2], the authors develop a global correspondence between immersed weakly horospherically convex hypersurfaces $phi:M^n to mathbb{H}^{n+1}$ and a class of conformal metrics on domains of the round sphere $mathbb{S}^n$. Some of the key aspects of th
It is known that for $Omega subset mathbb{R}^{2}$ an unbounded convex domain and $H>0$, there exists a graph $Gsubset mathbb{R}^{3}$ of constant mean curvature $H$ over $Omega $ with $partial G=$ $partial Omega $ if and only if $Omega $ is included i