Title: Properties of Busemann function on manifolds with nonnegative sectional curvature outside of a compact set

Date: 11/11/2019

Time: 3:00 PM - 3:50 PM

Place: C304 Wells Hall

Busemann functions are useful. Cheeger and Gromoll used them to prove the splitting theorem for manifolds with nonnegative ricci curvature that contains a line. Yau used them to prove that complete noncompact manifolds with nonnegative Ricci curvature have at least linear volume growth.
In a paper called "Positive Harmonic Functions on Complete Manifolds with Non-Negative Curvature Outside a Compact Set" Peter Li and Luen-Fai Tam also used Busemann function to show the existence of positive harmonic functions. I will talk about Li and Tam's proof of properties of Busemann function. The proof only uses Toponogov theorem and cosine law. The results of the proof is useful for the subsequent analysis part of the paper.