Complete nonnegatively curved planes

Geometry Topology Seminar
Monday, September 9, 2013 - 14:05
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
It is known that any complete nonnegatively curved metric on the plane is conformally equivalent to the Euclidean metric. In the first half of the talk I shall explain that the conformal factors that show up correspond precisely to smooth subharmonic functions of minimal growth. The proof is function-theoretic. This characterization of conformal factors can be used to study connectedness properties of the space of complete nonnegatively curved metrics on the plane. A typical result is that the space of metrics cannot be separated by a finite dimensional subspace. The proofs use infinite-dimensional topology and dimension theory. This is a joint work with Jing Hu.