Geometric barriers for the existence of hypersurfaces with prescribed curvatures in \(\mathbb M^n\times\mathbb R\) (Q745597)

From the abstract: We show the existence of a deformation process of hypersurfaces from a product space \(\mathbb{M}_{1} \times \mathbb{R}\) into another product space \(\mathbb{M}_{2} \times \mathbb{R}\) such that the relation of the principal curvatures of the deformed hypersurfaces can be controlled in terms of the sectional curvatures or Ricci curvatures of \(\mathbb{M}_{1}\) and \(\mathbb{M}_{2}\). In this way, we obtain barriers which are used for proving existence or non existence of hypersurfaces with prescribed curvatures in a general product space \(\mathbb{M} \times \mathbb{R}\).