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math.CV2026
A Criterion for the Sphericity of a CR Manifold
M. A. Stepanova
We formulate and prove a simple criterion for the sphericity of a CR manifold (that is, for its equivalence to its model surface). We discuss the differences between the general ca…
math.CV2026
Invariants of singular germs of real-analytic sets
M. A. Stepanova
New biholomorphic invariants of a germ of a real-analytic set at a singular point (either an RC-singular point or a singular point of a smooth structure) are found: the Bloom-Graha…
math.CV2026
The Dimension Conjecture for 2-Nondegenerate Hypersurfaces
M. A. Stepanova
The dimension conjecture in CR geometry is proved for 2-nondegenerate real-analytic hypersurfaces with sign-definite Levi form. Namely, it is proved that, in the indicated class of…