Complete nonnegatively curved planes

Series: 
Geometry Topology Seminar
Monday, September 9, 2013 - 14:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Georgia Tech
Organizer: 
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.