We present a new proof of the sphere covering inequality in the spirit of comparison geometry, and as a by-product we find another sphere covering inequality that can be viewed as the dual of the original one. We also prove sphere covering inequalities on surfaces satisfying general isoperimetric inequalities, and discuss their applications to elliptic equations with exponential nonlinearities in dimension 2. The approach in this paper extends, improves, and unifies several inequalities about solutions of elliptic equations with exponential nonlinearities.
ASJC Scopus subject areas
- Applied Mathematics