Complete Kahler Manifolds with Bounded Geometry

Mohan Ramachandran
SUNY/Buffalo and Utah

Saturday, April 29
3:30PM

The study of bounded-geometry complete Riemannian metrics on smooth manifolds is well understood, since any smooth manifold admits such a metric by a theorem of Robert Greene. The existence of such metrics in the Kahler context leads to obstructions of various kinds. I will be talking about this. A sample theorem is as follows. Let M be a complete Kahler manifold with bounded geometry and connected.

Theorem:

  1. If H^1(M,R)=0, then M has at most one end.
  2. If M has at least three ends then M maps holomorphically onto a Riemann surface.

All of this is joint work with T. Napier. The technique used to prove these results is based on the theory of harmonic functions on these manifolds.

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Suggestions or corrections to

Jack Lee <lee@math.washington.edu>.