论文标题
在度量空间中关键指数的对称和紧凑型嵌入
Symmetry and compact embeddings for critical exponents in metric-measure spaces
论文作者
论文摘要
我们在紧凑的度量空间中获得了一个紧凑的Sobolev嵌入功能，其中$ h $是保留近距离的小组的子组。在Riemannian歧管中，$ h $是保留差异的卷的子组：接下来是关键指数的紧凑型嵌入。结果可以看作是在紧凑型歧管中异分析下函数不变的sobolev嵌入的扩展。
We obtain a compact Sobolev embedding for $H$-invariant functions in compact metric-measure spaces, where $H$ is a subgroup of the measure preserving bijections. In Riemannian manifolds, $H$ is a subgroup of the volume preserving diffeomorphisms: a compact embedding for the critical exponents follows. The results can be viewed as an extension of Sobolev embeddings of functions invariant under isometries in compact manifolds.
