In this paper, an analogue of Bieberbach’s distortion theorem has been proposed, in a class quasi-conformal maps.

In a previous paper, we proved that quasi-isometric map $$f:X\rightarrow Y$$ between two pinched Hadamard manifolds X and Y is within bounded distance from unique harmonic map. We extend this result to maps $$f:\Gamma \backslash X\rightarrow , where $$\Gamma $$ convex cocompact discrete group of isometries f locally at infinity.

Microinstabilities such as ion temperature gradient (ITG) mode and trapped electron (TEM) in quasi-axisymmetric (QA) stellarator are investigated by using gyrokinetic Vlasov simulations, where the QA configuration of Chinese first is utilized. Extensive parameter scans with respect to density gradients for zero beta cases identify microinstability maps that indicate transition boundary among IT...

We obtain a very simple formula for the generating function of bipartite (resp. quasi-bipartite) planar maps with boundaries (holes) of prescribed lengths, which generalizes certain expressions obtained by Eynard in a book to appear. The formula is derived from a bijection due to Bouttier, Di Francesco and Guitter combined with a process (reminiscent of a construction of Pitman) of aggregating ...