On unique extremality
On unique extremality
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DOI：
10.1080/17476939908815215
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发表时间：
1999-12
影响因子：
0.9
通讯作者：
Yu-Liang Shen
中科院分区：
文献类型：
--
作者：
Yu-Liang Shen
设M（R）表示Riemann曲面R上所有本质有界Beltrami微分空间L∞（R）的单位球.众所周知，μ∈M（R）是无穷小极值的当且仅当μ/（1-|μ| 2）∈L∞（R）是无穷小极值。本文证明了对于唯一极值，类似的结果也成立，即μ∈M（R）是唯一无穷小极值的当且仅当μ/（1-|μ| 2）∈L∞（R）是唯一无穷小极值。并给出了应用实例。
Let M(R) denote the unit ball of the space L∞(R) of all essentially bounded Beltrami differentials on a Riemann surface R. It is well known that μ∈M(R) is infinitesimally extremal if and only if μ/(1−|μ|2)∈L∞(R) is infinitesimally extremal. In this paper, it is proved that the analogous result holds for the unique extremality, that is, μ∈M(R) is uniquely infmitesimally extremal if and only if μ/(1−|μ|2)∈L∞(R) is uniquely infinitesimally extremal. An application is also given.