Nonnegativity of the CR Paneitz operator for embeddable CR manifolds

Y Takeuchi - 2020 - projecteuclid.org
The nonnegativity of the CR Paneitz operator plays a crucial role in three-dimensional CR
geometry. In this paper, we prove this nonnegativity for embeddable CR manifolds. This …

Improved higher-order Sobolev inequalities on CR sphere

Z Yan - Journal of Functional Analysis, 2023 - Elsevier
We improve higher-order CR Sobolev inequalities on S 2 n+ 1 under the vanishing of higher
order moments of the volume element. As an application, we give a new and direct proof of …

ℐ'-curvatures in higher dimensions and the Hirachi conjecture

JS Case, Y Takeuchi - Journal of the Mathematical Society of Japan, 2023 - jstage.jst.go.jp
We construct higher-dimensional analogues of the I′-curvature of Case and Gover in all
CR dimensions n≥ 2. Our I′-curvatures all transform by a first-order linear differential …

Generalizations of the Q-prime curvature via renormalized characteristic forms

Y Takeuchi - Advances in Mathematics, 2023 - Elsevier
The Q-prime curvature is a local pseudo-Einstein invariant on CR manifolds defined by
Case and Yang, and Hirachi. Its integral, the total Q-prime curvature, gives a non-trivial …

-curvatures in higher dimensions and the Hirachi conjecture

JS Case, Y Takeuchi - arxiv preprint arxiv:2003.08201, 2020 - arxiv.org
We construct higher-dimensional analogues of the $\mathcal {I}^\prime $-curvature of Case
and Gover in all CR dimensions $ n\geq2 $. Our $\mathcal {I}^\prime $-curvatures all …