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Vinícius Novelli

Publications and source records attributed to Vinícius Novelli.

4 recordsLinked to original sources
arXiv2026

Global properties of the differential complex associated to closed, nonsingular $1$-forms on compact manifolds

Given a closed, real, non-singular 1-form on a compact manifold $Ω$, global properties of the associated differential complex are studied. We completely characterize global solvability in the first and last levels of the complex. Furthermore, in the particular case where the $1$-form is rational, we prove global solvability for every degree and give a complete description of the cohomology spaces. Finally, a complete characterization for global hypoellipticity is obtained, building on the work of A. Meziani (Comm. PDE., 2002). In all cases, it is shown that the conditions depend exclusively on the arithmetic nature of the form's periods.

math.AP↗
arXiv2026

Cohomology of CR structures on compact Lie groups

We show that, under a division condition, the tangential Cauchy--Riemann cohomology of a compact Lie group with a left-invariant CR structure can be computed on a suitable maximal torus. As a consequence, we conclude that the tangential Cauchy--Riemann cohomology is finite-dimensional. We also show that, for a class of CR structures, this division condition is necessary for the total cohomology to be finite-dimensional. The proof combines Fourier analysis on compact Lie groups, highest-weight representations and Lie algebra cohomology. This not only generalizes but provides completely new proofs for the analogous result due to Pittie and for its extensions to Levi-flat CR structures, obtained by Jacobowitz and Jahnke.

math.CV↗
arXiv2025

On the regularity of nondegenerate hypo-analytic structures of hypersurface type

For a smooth, non-degenerate locally integrable structure of hypersurface type on a manifold $M$, we provide necessary and sufficient conditions for it to be equivalent, near a point, to a real-analytic locally integrable structure (the analytic regularizability), generalizing a recent result of Zaitsev and the first author. First, we discover, in our setting, a (previously unknown) invariant CR submanifold $Σ$ in $M$ of hypersurface type, which we call the central submanifold. We prove that the analytic regularizability of $M$ is equivalent to that of the associated CR manifold $Σ$. Furthermore, as a byproduct of our construction, we show that the central manifold construction reduces the whole (smooth or analytic) equivalence problem for nondegenerate structures with the Levi positivity condition to that of the associated central manifolds, i.e. to CR geometry. Second, we make use of a classical construction due to Marson and show that sufficient for the analytic regularizability of $M$ is the analytic regularizability of the CR manifold $\tilde M$ associated with $M$ in the sense of Marson. We show applications of both regularizability conditions to classes of locally integrable structures.

math.CV↗