The Sphere Covering Inequality and Its Dual
The Sphere Covering Inequality and Its Dual
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DOI：
10.1002/cpa.21903
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发表时间：
2020-06
影响因子：
3
通讯作者：
C. Gui;Fengbo Hang;Amir Moradifam
中科院分区：
文献类型：
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作者：
C. Gui;Fengbo Hang;Amir Moradifam
我们本着比较几何的精神提出了一个涵盖不等式的领域的新证明，作为副产品，我们发现了另一个涵盖不等式的领域，它可以被视为原始领域的对偶。我们还证明了满足一般等周不等式的曲面上的球面覆盖不等式，并讨论了它们在二维指数非线性椭圆方程中的应用。本文的方法扩展、改进和统一了关于具有指数非线性椭圆方程解的几个不等式。 © 2020 Wiley 期刊有限责任公司
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