4 papers
Isometric submersions of Teichmüller spaces are forgetful
Dmitri Gekhtman, Mark Greenfield
We study the class of holomorphic and isometric submersions between finite-type Teichmüller spaces. We prove that, with potential exceptions coming from low-genus phenomena, any su…
Classifying complex geodesics for the Carathéodory metric on low-dimensional Teichmüller spaces
Dmitri Gekhtman, Vladimir Markovic
It was recently shown that the Carathéodory and Teichmüller metrics on the Teichmüller space of a closed surface do not coincide. On the other hand, Kra earlier showed that the met…
Asymptotics of the translation flow on holomorphic maps out of the poly-plane
Dmitri Gekhtman
We study the family of holomorphic maps from the polydisk to the disk which restrict to the identity on the diagonal. In particular, we analyze the asymptotics of the orbit of such…
Cyclic Pursuit on Compact Manifolds
Dmitri Gekhtman
We study a form of cyclic pursuit on Riemannian manifolds with positive injectivity radius. We conjecture that on a compact manifold, the piecewise geodesic loop formed by connecti…