The Sphere Covering Inequality and Its Dual |
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| Authors: | Changfeng Gui Fengbo Hang Amir Moradifam |
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| Institution: | 1. Department of Mathematics, The University of Texas at San Antonio, San Antonio, TX, 78249;2. Courant Institute, 251 Mercer Street, New York, NY, 10012 USA;3. Department of Mathematics, University of California, Riverside, CA, 92521 USA |
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| Abstract: | 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. © 2020 Wiley Periodicals LLC |
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