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Register a new userSchwarz type lemmas for pseudo-Hermitian manifolds
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In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds. These maps include the emph{CR} maps and the transversally holomorphic maps. In terms of some sub-Laplacian or Hessian type Bochner formulas, and comparison theorems in the pseudo-Hermitian version, we are able to establish several Schwarz type results for both the emph{CR} maps and the transversally holomorphic maps between pseudo-Hermitian manifolds. Finally, we also discuss the emph{CR} hyperbolicity problem for pseudo-Hermitian manifolds.
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In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds and Hermitian manifolds. By Bochner formulas and comparison theorems, we establish related Schwarz type results. As corollaries, Liouville theorem and little Picard theorem for basic CR functions are deduced. Finally, we study CR Caratheodory pseudodistance on CR manifolds.
In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish related Schwarz type lemmas for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce Liouville type theorems for almost holomorphic maps.
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Based on uniform CR Sobolev inequality and Moser iteration, this paper investigates the convergence of closed pseudo-Hermitian manifolds. In terms of the subelliptic inequality, the set of closed normalized pseudo-Einstein manifolds with some uniform geometric conditions is compact. Moreover, the set of closed normalized Sasakian $eta$-Einstein $(2n+1)$-manifolds with Carnot-Caratheodory distance bounded from above, volume bounded from below and $L^{n + frac{1}{2}}$ norm of pseudo-Hermitian curvature bounded is $C^infty$ compact. As an application, we will deduce some pointed convergence of complete Kahler cones with Sasakian manifolds as their links.
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