Best Lipschitz Maps and Transverse Measures - Part 2

Delve into the second part of a lecture series on best Lipschitz maps and transverse measures presented by Karen Uhlenbeck from the University of Texas at Austin. Explore a scheme for finding maps that realize the best Lipschitz constant between hyperbolic surfaces within a fixed homotopy class. Examine the use of Schatten-von Neumann norm approximations and discover how transverse measures with values in a Lie algebra bundle emerge from Noether's theorem. Investigate the connection between limiting transverse measures and infinitesimal earthquakes along canonical laminations, providing an analytic description of this geometric phenomenon. Gain insights into the relationship between length variation and earthquakes in Teichmuller theory, bridging concepts from geometric topology and differential geometry.