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math.DG2024
On minimal hypersurfaces in Euclidean spaces and Riemannian manifolds
Josef Mikes, Sergey Stepanov, Irina Tsyganok
This paper establishes the conditions under which minimal and stable minimal hypersurfaces are characterized as hyperplanes in Euclidean spaces and as totally geodesic submanifolds…
math.DG2023
New applications of the Ahlfors Laplacian
Sergey E. Stepanov, Josef Mikes, Irina I. Tsyganok
In this article, we consider an orthogonal decomposition of the traceless part of the Ricci tensor of a compact Riemannian manifold and study its application to the geometry of com…
math.DG2018
On higher order Codazzi tensors on complete Riemannian manifolds
I. G. Shandra, S. E. Stepanov
We prove several Liouville-type non-existence theorems for higher order Codazzi tensors and classical Codazzi tensors on complete and compact Riemannian manifolds, in particular. T…