The Sphere Covering Inequality and Its Dual

Changfeng Gui, Fengbo Hang, Amir Moradifam

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)2685-2707
Number of pages23
JournalCommunications on Pure and Applied Mathematics
Issue number12
StatePublished - Dec 1 2020

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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