Yuya Takeuchi

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20182020

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math.DG2020

$I^{'}$ -curvatures in higher dimensions and the Hirachi conjecture

Jeffrey S. Case, Yuya Takeuchi

We construct higher-dimensional analogues of the $I^{'}$ -curvature of Case and Gover in all CR dimensions $n \geq 2$ . Our $I^{'}$ -curvatures all transform b…

math.DG2019

Nonnegativity of the CR Paneitz operator for embeddable CR manifolds

Yuya Takeuchi

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 res…

math.DG2018

Stability of the existence of a pseudo-Einstein contact form

Yuya Takeuchi

A pseudo-Einstein contact form plays a crucial role in defining some global invariants of closed strictly pseudoconvex CR manifolds. In this paper, we prove that the existence of a…

math.DG2018

On the second variation of the Graham-Witten energy

Yuya Takeuchi

The area renormalization procedure gives an invariant of even-dimensional closed submanifolds in a conformal manifold, which we call the Graham-Witten energy, and it is a generaliz…

I′-curvatures in higher dimensions and the Hirachi conjecture

Nonnegativity of the CR Paneitz operator for embeddable CR manifolds

Stability of the existence of a pseudo-Einstein contact form

On the second variation of the Graham-Witten energy

$I^{'}$ -curvatures in higher dimensions and the Hirachi conjecture