Volumes and areas of Lipschitz metrics
Volumes and areas of Lipschitz metrics
复制标题
Lipschitz 度量的体积和面积
DOI：
10.1090/s1061-0022-09-01053-x
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发表时间：
2009
影响因子：
0.8
通讯作者：
S. Ivanov
中科院分区：
文献类型：
--
作者：
S. Ivanov
我们发展和推广了利用非扩张映射估计（黎曼和芬斯勒）填充体积的方法到L∞型Banach空间.对于每个Finsler体积泛函（如Busemann体积或Holmes-Thompson体积），我们构造了从Finsler度量类到所有Lipschitz度量的自然扩展，并定义了Banach空间中Lipschitz曲面的面积概念.建立了L∞型空间中极小填充与极小曲面之间的对应关系.我们引入了一个Finsler体积泛函，它的黎曼和Finsler填充体积是相等的，并证明了这个泛函是半椭圆的。
We develop and generalize methods of estimating (Riemannian and Finsler) filling volumes using nonexpanding maps to Banach spaces of L∞ type. For every Finsler volume functional (such as the Busemann volume or the Holmes–Thompson volume) we construct a natural extension from the class of Finsler metrics to all Lipschitz metrics and define the notion of area for Lipschitz surfaces in a Banach space. We establish a correspondence between minimal fillings and minimal surfaces in L∞ type spaces. We introduce a Finsler volume functional for which Riemannian and Finsler filling volumes are equal and prove that this functional is semi-elliptic.