Abstract

In this talk, we will give an informal report on frequency function that aims to cover the following things:

1. Basic case: frequency function for a harmonic function in Euclidean space.

2. How to generalize this method to a Riemannian manifold.

3. Some important problems using frequency function method (Survey)

     i. Unique continuation (Garofalo, Lin 1986)

     ii. Harmonic function with polynomial growth (Colding, Minicozzi 1997)

     iii. Positive mass theorem (Schoen, Yau 2017)

     iv. Vanishing order of eigenfunction (Mangoubi 2013).