In these notes, we collect the main and, to the best of our knowledge, most up-to-date achievements concerning the Bernstein problem in the Heisenberg group; that is, the problem of determining whether the only entire minimal graphs are hyperplanes. We analyze separately the problem for t-graphs and for intrinsic graphs: in the first case, the Bernstein Conjecture turns out to be false in any dimension, and a complete characterization of minimal graphs is available in H1 for the smooth case. A positive result is instead available for Lipschitz intrinsic graphs in H1; moreover, one can see that the conjecture is false in Hn with n at least 5, by adapting the Euclidean counterexample in high dimension; the problem is still open when n is 2, 3...
AbstractWe describe intrinsically regular submanifolds in Heisenberg groups Hn. Low dimensional and ...
We prove that Lipschitz intrinsic graphs in the Heisenberg groups ℍn, with n \u3e 1, which are vanis...
We develop a surface theory in pseudohermitian geometry. We define a notion of (p-)mean curvature an...
In the paper [13] we proved that the only stable C 2 minimal surfaces in the first Heisenberg group ...
In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-Carathéodory (C...
One of the main objectives of this paper is to unravel it new interesting phenomenon of the sub-Riem...
A negative answer to the Bernstein problem for entire H-perimeter minimizing intrinsic graphs is giv...
This is a note based on the paper [32] written in collaboration with M. Ritoré. The purpose of this ...
We classify the entire minimal vertical graphs in the Heisenberg group Nil3 endowed with a Riemannia...
We construct nonlinear entire anisotropic minimal graphs over $\mathbb{R}^4$, completing the solutio...
This work is divided into two, largely independent parts. The first discusses so-called two-valued m...
In the setting of the sub-Riemannian Heisenberg group H^n, we introduce and study the classes of t- ...
In the first Heisenberg group H-1 with its sub-Riemannian structure generated by the horizontal subb...
Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian ...
In this note we present a simple alternative proof for the Bernstein problem in the threedimensional...
AbstractWe describe intrinsically regular submanifolds in Heisenberg groups Hn. Low dimensional and ...
We prove that Lipschitz intrinsic graphs in the Heisenberg groups ℍn, with n \u3e 1, which are vanis...
We develop a surface theory in pseudohermitian geometry. We define a notion of (p-)mean curvature an...
In the paper [13] we proved that the only stable C 2 minimal surfaces in the first Heisenberg group ...
In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-Carathéodory (C...
One of the main objectives of this paper is to unravel it new interesting phenomenon of the sub-Riem...
A negative answer to the Bernstein problem for entire H-perimeter minimizing intrinsic graphs is giv...
This is a note based on the paper [32] written in collaboration with M. Ritoré. The purpose of this ...
We classify the entire minimal vertical graphs in the Heisenberg group Nil3 endowed with a Riemannia...
We construct nonlinear entire anisotropic minimal graphs over $\mathbb{R}^4$, completing the solutio...
This work is divided into two, largely independent parts. The first discusses so-called two-valued m...
In the setting of the sub-Riemannian Heisenberg group H^n, we introduce and study the classes of t- ...
In the first Heisenberg group H-1 with its sub-Riemannian structure generated by the horizontal subb...
Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian ...
In this note we present a simple alternative proof for the Bernstein problem in the threedimensional...
AbstractWe describe intrinsically regular submanifolds in Heisenberg groups Hn. Low dimensional and ...
We prove that Lipschitz intrinsic graphs in the Heisenberg groups ℍn, with n \u3e 1, which are vanis...
We develop a surface theory in pseudohermitian geometry. We define a notion of (p-)mean curvature an...