Alaa Boukholkhal

collaborators

3 papers

math.DG2026

The $1$ -parametric $h$ -principle for smooth conformal immersions of surfaces

Alaa Boukholkhal

We reformulate the problem of finding conformal immersions of closed Riemannian surfaces in the language of the $h$ -principle and we prove that the inclusion from the space of smoo…

math.DG2025

$C^{1}$ -isometric embeddings of Riemannian spaces in Lorentzian spaces

Alaa Boukholkhal

For any compact Riemannian manifold $(V, g)$ and any Lorentzian manifold $(W, h)$ , we prove that any spacelike embedding $f : V \to W$ that is long ( $g \leq f^{*} h$ ) can be $C^…

math.DG2025

Flexibility and rigidity of conformal embeddings in Lorentzian manifolds

Alaa Boukholkhal

We prove that for any Riemannian metric $g$ on a closed orientable surface $I^£$ and any spacelike embedding $f : I^£ \to M$ in a pseudo-Riemannian manifold $(M, h)$ , the embeddi…

The 1-parametric h-principle for smooth conformal immersions of surfaces

C1-isometric embeddings of Riemannian spaces in Lorentzian spaces

Flexibility and rigidity of conformal embeddings in Lorentzian manifolds

The $1$ -parametric $h$ -principle for smooth conformal immersions of surfaces

$C^{1}$ -isometric embeddings of Riemannian spaces in Lorentzian spaces