An Optimal Gap Theorem in a complete strictly pseudoconvex CR (2n+1)-manifold


Yen-Wen Fan

10:30:00 - 12:00:00

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

In this talk, we apply a linear trace Li-Yau-Hamilton inequality for a positive (1,1)-form solution of the CR Hodge-Laplace heat equation and monotonicity of the heat equation deformation, we obtain an optimal gap theorem for a complete strictly pseudoconvex CR (2n+1)-manifold with nonnegative pseudohermitian bisectional curvature and vanishing torsion. We will prove that if the average of the Tanaka-Webster scalar curvature over a ball of radius r centered at any fixed point o dacays as o(r-2), then the manifold is flat.