The sphere covering inequality and its dual

Abstract

We present a new proof of the sphere covering inequality in the spirit of comparison geometry, and as a byproduct we find another sphere covering inequality which 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 two. The approach in this paper extends, improves, and unifies several inequalities about solutions of elliptic equations with exponential nonlinearities.

21 pages

References in corpus (3)

• The sphere covering inequality and its dual
• Mean field equations, hyperelliptic curves and modular forms: I
• Uniqueness of the Mean Field Equation and Rigidity of Hawking Mass

Cited by in corpus (6)

• The sphere covering inequality and its dual
• Remarks on a mean field equation on ${\mathbb{S}}^2$
• Improved Beckner's inequality for axially symmetric functions on ${\mathbb{S}}^n$
• Entropy maximization in the two-dimensional Euler equations
• Existence results for a generalized mean field equation on a closed Riemann surface
• Existence results for a non-relativistic Chern-Simons model with purely mutual interaction