Mahan Mj

We will start by providing two kinds of motivation for the 
study of Cannon-Thurston maps: the first classical differential 
geometric, involving the extrinsic geometry of surfaces in 3-space; the 
second from complex dynamics involving landing rays.

For a hyperbolic subgroup H of a hyperbolic group G, we shall then 
describe sufficient criteria to guarantee the following two conditions
a) Geodesic rays in H starting at 1 land at a unique point of the 
boundary of G
b) The inclusion of H in G does not extend continuously to the boundary
As a consequence we obtain diverse classes of examples demonstrating the 
non-existence of Cannon-Thurston maps. These include the Baker-Riley 
examples.
This is joint work with Rakesh Halder and Pranab Sardar.