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Given $Hin [0,1)$ and given a $C^0$ exterior domain $Omega$ in a $H-$hypersphere of $mathbb{H}^3,$ the existence of hyperbolic Killing graphs of CMC $H$ defined in $overline{Omega}$ with boundary $ partial Omega $ included in the $H-$hypersphere is obtained.
Let $M$ be a compact constant mean curvature surface either in $mathbb{S}^3$ or $mathbb{R}^3$. In this paper we prove that the stability index of $M$ is bounded below by a linear function of the genus. As a by product we obtain a comparison theorem b
The Han-Li conjecture states that: Let $(M,g_0)$ be an $n$-dimensional $(ngeq 3)$ smooth compact Riemannian manifold with boundary having positive (generalized) Yamabe constant and $c$ be any real number, then there exists a conformal metric of $g_0$
We prove the mean curvature flow of a spacelike graph in $(Sigma_1times Sigma_2, g_1-g_2)$ of a map $f:Sigma_1to Sigma_2$ from a closed Riemannian manifold $(Sigma_1,g_1)$ with $Ricci_1> 0$ to a complete Riemannian manifold $(Sigma_2,g_2)$ with bound
We first present a warped product manifold with boundary to show the non-uniqueness of the positive constant scalar curvature and positive constant boundary mean curvature equation. Next, we construct a smooth counterexample to show that the compactn
We show that under certain curvature conditions of the ambient space an entire Killing graph of constant mean curvature lying inside a slab must be a totally geodesic slice.