The Li-Yau Eigenvalue Estimates and CR Obata Theorem in Pseudohermitian Manifolds


Shu-Cheng Chang 

15:00  - 15:50 

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, based on a jointed work with Hung-Lin Chiu, we first have the CR analogue of Li-Yau's eigenvalue estimate on the lower bound estimate of psitive first eigenvalue of the sub-Laplacian in pseudohermitian $(2n+1)$-manifolds. Second, we prove the CR Obata's theorem on a closed pseudohermitian manifold with vanishing torsion. The key step is a discovery of CR analogue of Bochner formula which involving the CR Paneitz operator and nonnegativity of CR Paneitz operator for any closed pseudohermitian $(2n+1)$-manifold with $n>1$.