Related papers: Prescribing the curvature to Killing Graphs

It is proved the existence and uniqueness of Killing graphs with prescribed mean curvature in a large class of Riemannian manifolds.

It is proved the existence and uniqueness of graphs with prescribed mean curvature in Riemannian submersions fibered by flow lines of a vertical Killing vector field.

We prove the existence and uniqueness of graphs with prescribed mean curvature function in a large class of Riemannian manifolds which comprises spaces endowed with a conformal Killing vector field.

We extend the interior gradient estimate due to N. Korevaar and L. Simon for solutions of the mean curvature equation from the case of Euclidean graphs to the general case of Killing graphs. Our main application is the proof of existence of…

We prove an existence result for helicoidal graphs with prescribed mean curvature in a large class of warped product spaces which comprises space forms.

We obtain height, gradient, and curvature a priori estimates for a modified mean curvature flow in Riemannian manifolds endowed with a Killing vector field. As a consequence, we prove the existence of smooth, entire, longtime solutions for…

We study the asymptotic Dirichlet problem for Killing graphs with prescribed mean curvature $H$ in warped product manifolds $M\times_\varrho \mathbb{R}$. In the first part of the paper, we prove the existence of Killing graphs with…

We study a Neumann problem related to the evolution of graphs under mean curvature flow in Riemannian manifolds endowed with a Killing vector field. We prove that in a particular case these graphs converge to a bounded minimal graph which…

In this paper, we provided conditions for an entire constant mean curvature Killing graph lying inside a possible unbounded region to be necessarily a slice.

We develop a conformal duality for spacelike graphs in Riemannian and Lorentzian three-manifolds that admit a Riemannian submersion over a Riemannian surface whose fibers are the integral curves of a Killing vector field, which is timelike…

We prove that there exist solutions for a non-parametric capillary problem in a wide class of Riemannian manifolds endowed with a Killing vector field. In other terms, we prove the existence of Killing graphs with prescribed mean curvature…

A priori estimates for the mean curvature evolution of Killing graphs in Cartan-Hadamard manifolds with asymptotic Dirichlet conditions are established. As an application, the existence of the corresponding parabolic flow is proved,…

We study the prescribed mean curvature equation for $t$-graphs in a Riemannian Heisenberg group of arbitrary dimension. We characterize the existence of classical solutions in a bounded domain without imposing Dirichlet boundary data, and…

We prove the existence and uniqueness of radial graphs over a given domain of $\mathbb{S}^{n}$ having boundary on the sphere $\mathbb{S}^{n}$ and whose mean curvature at every point equals a prescribed positive function satisfying suitable…

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.

The purpose of this paper is twofold: firstly, to establish sufficient conditions under which the mean curvature flow supported on a hypersphere with exterior Dirichlet boundary exists globally in time and converges to a minimal surface,…

Let $\mathbb{E}$ be a connected and orientable Riemannian 3-manifold with a non-singular Killing vector field whose associated one-parameter group of the isometries of $\mathbb{E}$ acts freely and properly on $\E$. Then, there exists a…

Prescribed mean curvature problems on the torus has been considered in one dimension. In this paper, we prove the existence of a graph on the $n$-dimensional torus $\mathbb {T}^n$, the mean curvature vector of which equals the normal…

This survey describes some recent rigidity results obtained by the authors for the prescribed mean curvature problem on graphs $u : M \rightarrow \mathbb{R}$. Emphasis is put on minimal, CMC and capillary graphs, as well as on graphical…

This paper continues the investigation of isoperimetric inequalities through volume preserving and area decreasing mean curvature type flows related to conformal Killing vector fields. Results of this kind prior to this paper all studied…