arXiv subjects

Stepanov Sergey

Publications and source records attributed to Stepanov Sergey.

3 recordsLinked to original sources

arXiv2026

Harmonic Gauge on the Space of Riemannian Metrics and Its Role in the Ricci-DeTurck Flow

We develop a harmonic gauge on the space of Riemannian metrics and study its role in the variational and flow-theoretic structure of geometric analysis. We prove that the harmonic gauge eliminates divergence-type terms in the first variation of the Hilbert-Einstein functional and induces a natural elliptic structure for the second variation. As a consequence, positivity of the curvature operator of the second kind implies spectral stability of the functional. This establishes a conceptual link between gauge fixing, elliptic operator theory, and geometric rigidity, and provides a variational counterpart to the Ricci-DeTurck mechanism.

math.DG↗

arXiv2016

A Liouvile-type theorems for some classes of complete Riemannian almost product manifolds and for special mappings of complete Riemannian manifolds

In the present paper we prove Liouville-type theorems: non-existence theorems for some complete Riemannian almost product manifolds and special mappings of complete Riemannian manifolds which generalize similar results for compact manifolds.

math.DG↗

arXiv2015

Two examples of eigenforms of the Hodge-de Rham Laplacian

In the present paper, we consider the Hodge-de Rham Laplacian that acts on conformal Killing and projective Killing one-forms of a compact Riemannian manifold.

math.DG↗