Symmetry and compact embeddings for critical exponents in metric-measure spaces
Differential Geometry
2020-02-04 v1
Abstract
We obtain a compact Sobolev embedding for -invariant functions in compact metric-measure spaces, where is a subgroup of the measure preserving bijections. In Riemannian manifolds, 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.
Keywords
Cite
@article{arxiv.2002.00076,
title = {Symmetry and compact embeddings for critical exponents in metric-measure spaces},
author = {M. Gaczkowski and P. Górka and D. J. Pons},
journal= {arXiv preprint arXiv:2002.00076},
year = {2020}
}