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 …
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 …
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
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 …
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 …
Case and Yang, and Hirachi. Its integral, the total Q-prime curvature, gives a non-trivial …
-curvatures in higher dimensions and the Hirachi conjecture
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 …
and Gover in all CR dimensions $ n\geq2 $. Our $\mathcal {I}^\prime $-curvatures all …